Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Log Help

  1. Mar 1, 2005 #1
    Hey... requested my professor to give me a few word problems to enable me to improve my skills... am having problems solving them however and was hoping that you could guys could help me:

    Q1) Use a calculator to evaluate the following powers. Round the results to five decimal placeS. Each of these powers has a rational exponent. Explain how you can use these powers to define 3^( sqrt of 2 ) which has an irrational exponent.

    3^(14/10) = 4.65554
    3^(141/100)=4.70697
    3^(1414/10000)= 4.72770
    3^(14142/10000)= 4.72873
    3^(141421/100000)= 4.72878
    3^(1414213/1000000)= 4.72880


    3^( sqrt of 2 ) = 4.728804

    so basically the value of 3^(sqrt of 2 ) comes after 3^(1414213/1000000)... hence, you could find the log of 3^14/10 which is .6679697566, then probably do the following : 3^(.667..+.667...+.667....+.667.. +.667 +.667.. +.667).

    EDIT: damn .. what i did above doesnt make sense.. im soo confused.!!! i do know that i can somehow use logs by finding the log of one value and then adding the solution multiple times to find the value of 3^ ( sqrt of 2 )

    _________________________________________________________

    Question 2:

    Find a value of n for which (1+1/n)^n gives the value of e correct to 9 decimal places. Explain the process you used to find your answer.

    log 2.718281828 = log ( 1+1/n)^n
    log 2.718281828= n log ( 1+1/n)
    log 2.718281828/ log (1+1/n ) = n

    would that be the final answer?

    thanks
     
    Last edited: Mar 1, 2005
  2. jcsd
  3. Mar 1, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    DO NOT DOUBLE POST!!For your second problem,u could use a calculator which would give u 10 decimals of "e" (incidentally those are (2.)7182818284(59045...)) (why 10?If you write only 9,u'll never be sure if your calculator will not approximate the 9-th to a unit too much;...79... could be approximated to ...8...) and then use the calculator to give "n" and then find that "n" for which that "8" (the 9-th correct decimal) would appear.

    As for alternative solutions,they involve approximations,e.g. the one with the natural logarithm that u found...

    Daniel.
     
  4. Mar 1, 2005 #3
    imo, i cannot delete the previous topic that i made by mistake and hence need a mod to delete it... sorry for double posting.. didnt do it intentionally..

    how?????? even if i do try using 10 decimals of "e", how do i find the value of n??

    if i divide log "e" by log (1+1/n) i dont get anything... it comes up as being undefined..
     
  5. Mar 1, 2005 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Plug 10000.Here's what Maple had to say...2\,71814\,59268\,25224\,86403\,76646\,74913\,14653\,61138\,22649\,22072\,08183\,70865\,87378\,74197\,73771\,51396\,84730\,52781\,47783\,95201\,39855\,02523\,32514\,27278\,51252\,60669\,48976\,10003\,45427\,31187\,99109\,30676\,84981\,85665\,58206\,31434\,30483\,15259\,13526\,35090\,09396\,74095\,16117\,83827\,54701\,95160\,84152\,56234\,06623\,52454\,30366\,88228\,24462\,79113\,55300\,03628\,76646\,77326\,89431\,89206\,81691\,97525\,60437\,44118\,02619\,08090\,91242\,59954\,30139\,97331\,08900\,22516\,98440\,41752\,78311\,74265\,78254\,09053\,90869\,80995\,48471\,29021\,21665\,66588\,14625\,02271\,09169\,30414\,86593\,95043\,47113\,79360\,52635\,68619\,07204\,44341\,56650\,62312\,57307\,27145\,23371\,85859\,25169\,53304\,55204\,03164\,34171\,68712\,60201\,72171\,72825\,93982\,17597\,84770\,20199\,57286\,95047\,49610\,40780\,04870\,02090\,32684\,74828\,74211\,21504\,22562\,54506\,87128\,56837\,13569\,95235\,62847\,28296\,00130\,50103\,42072\,35344\,28402\,01207\,89837\,77823\,60731\,81136\,68753\,84354\,94239\,76305\,58814\,38020\,86993\,25390\,65124\,41050\,53034\,49906\,95514\,34511\,90839\,77979\,10008\,09300\,12129\,04329\,37146\,61240\,80514\,25607\,88507\,98122\,14852\,95384\,61005\,33365\,52966\,88636\,37769\,24886\,56701\,33871\,09186\,11213\,66257\,28522\,34189\,95744\,36261\,24608\,81383\,89040\,39103\,47556\,92955\,05398\,27066\,76308\,91155\,64368\,49477\,96282\,48213\,18982\,19724\,58728\,59148\,86874\,37150\,50913\,87331\,43934\,11326\,43378\,90590\,77061\,58998\,17768\,33014\,23090\,31857\,88496\,81830\,59127\,20085\,51962\,01516\,42029\,15007\,40823\,01080\,00533\,00309\,39446\,77178\,75440\,50622\,39152\,50225\,64804\,04709\,60629\,68846\,85359\,74408\,99934\,22869\,18821\,32079\,87556\,13196\,27792\,09151\,35200\,23003\,06799\,53130\,48886\,93014\,99903\,49526\,60063\,68565\,86012\,52445\,89661\,01252\,16587\,03414\,89802\,15349\,34053\,72500\,92978\,23494\,18564\,07359\,21744\,38229\,90375\,20681\,77138\,28176\,71004\,20574\,91049\,95053\,47137\,26133\,73757\,83167\,26475\,52891\,48022\,05071\,48746\,03377\,20422\,05470\,59003\,99501\,34136\,57320\,01149\,74901\,91705\,72280\,50672\,96291\,16623\,25841\,50517\,61038\,50715\,17465\,63807\,70271\,36701\,51492\,12059\,64151\,57841\,17228\,50703\,72096\,65769\,96944\,21790\,94434\,58628\,98694\,55420\,52788\,17213\,53742\,66993\,17363\,68990\,03818\,05354\,01160\,66617\,43530\,46462\,70416\,56958\,74738\,48354\,62814\,59251\,54486\,23983\,51932\,98400\,38644\,89009\,96908\,19530\,39220\,53429\,66500\,15373\,25249\,40861\,59997\,24080\,87961\,75141\,58253\,00934\,81846\,29286\,48728\,66034\,46820\,68093\,01185\,42220\,33016\,72361\,27557\,97781\,82285\,86757\,27242\,39316\,89786\,88276\,01904\,50817\,89416\,21178\,33401\,93288\,05230\,82487\,59224\,95028\,23139\,57113\,73366\,01266\,23158\,18074\,22154\,69139\,23909\,91505\,29407\,43253\,82597\,40573\,22201\,71483\,13598\,09131\,30381\,95870\,39205\,63395\,10850\,88058\,49011\,69265\,59161\,93555\,44122\,41090\,60053\,25004\,67993\,10239\,84146\,37463\,79029\,83587\,92006\,19505\,88708\,93770\,08735\,26543\,90124\,88785\,03126\,45257\,34217\,70426\,04927\,76552\,83383\,52771\,24892\,65936\,09383\,97637\,50798\,48922\,24035\,84655\,15434\,01428\,58341\,16758\,25501\,03554\,60901\,75655\,02433\,51670\,66365\,14615\,27156\,72111\,22306\,12440\,86896\,74738\,18565\,84631\,20175\,66515\,16753\,34083\,02696\,92173\,74013\,41727\,21587\,49267\,71276\,81241\,86793\,58458\,68236\,26026\,60001\,11617\,67151\,46171\,17344\,06182\,10950\,10285\,25480\,23708\,76594\,84278\,18985\,13148\,10362\,30322\,53898\,70805\,56557\,35180\,70652\,03104\,74230\,51098\,56838\,22945\,71577\,58594\,20389\,50586\,91510\,41904\,71845\,22532\,14233\,22379\,71245\,12543\,09735\,28153\,87062\,65259\,48582\,29607\,84917\,26627\,79027\,94961\,53801\,12002\,18829\,08295\,05218\,83314\,24449\,31369\,32268\,14353\,17342\,24264\,33438\,95563\,45324\,80757\,16186\,11150\,11047\,74404\,17242\,15497\,32231\,99825\,41754\,23415\,60084\,28899\,60784\,67878\,02354\,39265\,43299\,67488\,44279\,05227\,73325\,79052\,07486\,33817\,88831\,04518\,63699\,35213\,81997\,73563\,80230\,58403\,03018\,58735\,97302\,58317\,81150\,81414\,36924\,70549\,89104\,03291\,09530\,27328\,59576\,97403\,57672\,66189\,51041\,24886\,51551\,19119\,02994\,99858\,53614\,69145\,78153\,88613\,87131\,05135\,39191\,41747\,85937\,34983\,25497\,32369\,89862\,12084\,00725\,12206\,55957\,66548\,86372\,83220\,76982\,75789\,56905\,33463\,23927\,55559\,90909\,40142\,06007\,19007\,32569\,84026\,32702\,87110\,48930\,62730\,11638\,28384\,35207\,35557\,60248\,27023\,79019\,34425\,88028\,24866\,23395\,42326\,07958\,80814\,55498\,60205\,87350\,88230\,01638\,29703\,93886\,45916\,52392\,88565\,84635\,84975\,84682\,02701\,32247\,37979\,27035\,65787\,80073\,08286\,76842\,07199\,40647\,60112\,65343\,05710\,31458\,08664\,85760\,52919\,18589\,34650\,33678\,19801\,71890\,56241\,93902\,05938\,92677\,03082\,55477\,97285\,34941\,61370\,30689\,12446\,51495\,47472\,49099\,00019\,97660\,28835\,75422\,48041\,37487\,28405\,38191\,03940\,83261\,30499\,13477\,85572\,86606\,23170\,22143\,90262\,14903\,67476\,96073\,82313\,17784\,15881\,04025\,98196\,96293\,35455\,97731\,16668\,71148\,63971\,77212\,82028\,74911\,22546\,81060\,57744\,84733\,14716\,88312\,09035\,68785\,76921\,09996\,29470\,48211\,44267\,09354\,82407\,78417\,02545\,67979\,78804\,68499\,38891\,90982\,33226\,72831\,22527\,38254\,59932\,32003\,55398\,73479\,55178\,66212\,49110\,76208\,35010\,85812\,05272\,31682\,13137\,82695\,07067\,98878\,16903\,65683\,53433\,20601\,71482\,30952\,69592\,90968\,31595\,76139\,75375\,76594\,37204\,33862\,70583\,55641\,14162\,34618\,99899\,43779\,36625\,68729\,89877\,41790\,10340\,68129\,45853\,49415\,25253\,02532\,57478\,09808\,02308\,57993\,46679\,05050\,92561\,41136\,50702\,84661\,98049\,70683\,84996\,98996\,92419\,27669\,58576\,82762\,95428\,90208\,80559\,86419\,67533\,14845\,19446\,57818\,17084\,64989\,93519\,07321\,11196\,39674\,40919\,51629\,77065\,91279\,02241\,72899\,20997\,61926\,72423\,86602\,10513\,60434\,76165\,75235\,97000\,38102\,20485\,86312\,54514\,91328\,32918\,65217\,35318\,46272\,96920\,88331\,71738\,41908\,49172\,09989\,07820\,52585\,10704\,11068\,25501\,92668\,50489\,04138\,09443\,22976\,99895\,52757\,97807\,00666\,14076\,14120\,17780\,62116\,29753\,74591\,56303\,64518\,78526\,73608\,52898\,46493\,11728\,51182\,27148\,85229\,63483\,87500\,19891\,11879\,68774\,69578\,34234\,34298\,87171\,12917\,98499\,69088\,01424\,53465\,48810\,94690\,79645\,18710\,01247\,84291\,46815\,90979\,41793\,54918\,51788\,01752\,41752\,08766\,70616\,52844\,36332\,51763\,99704\,70891\,54244\,15007\,52335\,32501\,30469\,94030\,08716\,64429\,43215\,67226\,79316\,48256\,78925\,12411\,41548\,93225\,62785\,94250\,18835\,57928\,28846\,86536\,54049\,74541\,29353\,35738\,32483\,26568\,20477\,11294\,85663\,36472\,43143\,07362\,83319\,06397\,30372\,13331\,83866\,73400\,77812\,10432\,56771\,14991\,93554\,10159\,35324\,61174\,18416\,69107\,84243\,85612\,54128\,87672\,43003\,43210\,80659\,59957\,62722\,43287\,84121\,96312\,82829\,82520\,39025\,13818\,62383\,24316\,35864\,48958\,14781\,15757\,62617\,33679\,01432\,08303\,53754\,70493\,83523\,15730\,61808\,34986\,49304\,46781\,23831\,97169\,02619\,02082\,76509\,60382\,97629\,28710\,52705\,58757\,17833\,17520\,69713\,60037\,00575\,31824\,20635\,06931\,29582\,74738\,29983\,44968\,85781\,00356\,18186\,86837\,74039\,21384\,36623\,86082\,18312\,07649\,58069\,27437\,24852\,07739\,51726\,77764\,18430\,41375\,22098\,22114\,97661\,16616\,66807\,16071\,14764\,99569\,27388\,50867\,86704\,77433\,80444\,51578\,27569\,26232\,84191\,63600\,47921\,78227\,96497\,35365\,92769\,69004\,40399\,68889\,06549\,23746\,84313\,78488\,17956\,98737\,90524\,94060\,24375\,68629\,05326\,05605\,72757\,83586\,78630\,45827\,28408\,57296\,17642\,11527\,74314\,23896\,80623\,77102\,88516\,64536\,59522\,34294\,36485\,37127\,49275\,08359\,74062\,11774\,51129\,56147\,95154\,36623\,17845\,43994\,83148\,74068\,35795\,35448\,52216\,74194\,84562\,24441\,52589\,51182\,18045\,39494\,32406\,38263\,70562\,73076\,25542\,45636\,22944\,18423\,71837\,74862\,16435\,32490\,32340\,93414\,32079\,21522\,73654\,09937\,02060\,14551\,79586\,55787\,79665\,54233\,69582\,97239\,73574\,77682\,74406\,54273\,54758\,69706\,33669\,90030\,61555\,41762\,80553\,97053\,69950\,09654\,57091\,71900\,08932\,51698\,51554\,61231\,48926\,26656\,80030\,08039\,78200\,25824\,98319\,40027\,65214\,51939\,64530\,37703\,92446\,02110\,47714\,80114\,28006\,28215\,64988\,36906\,63664\,67683\,19942\,72358\,06466\,03449\,01768\,93482\,63828\,90857\,14470\,32684\,30788\,37470\,59013\,04566\,20815\,81564\,51452\,74422\,38543\,05208\,10881\,80650\,61270\,71484\,82414\,91964\,37339\,41858\,83683\,82425\,81631\,79355\,82707\,32984\,35214\,52937\,47634\,53554\,30479\,22498\,08808\,15741\,56236\,23280\,05255\,35528\,96867\,28712\,56418\,74003\,83651\,66561\,04134\,63037\,67348\,98783\,63544\,05401\,69117\,37663\,79231\,38785\,66390\,72035\,60297\,41703\,84415\,59048\,69922\,23462\,87901\,86731\,50921\,17100\,59418\,28328\,60740\,86811\,03181\,10313\,09604\,30447\,62051\,02745\,28659\,70970\,86869\,34415\,77149\,06308\,02259\,79608\,39284\,38935\,28324\,02328\,31282\,78398\,52847\,30173\,96782\,66677\,54879\,98880\,03856\,91192\,67613\,82472\,33227\,72887\,37404\,10523\,39258\,74574\,19865\,19878\,78948\,97003\,03637\,99244\,63718\,29254\,68002\,82983\,72048\,41765\,68240\,19368\,74047\,97154\,56002\,26243\,54689\,21350\,21776\,15373\,76634\,40310\,71181\,15371\,47103\,88040\,46070\,71367\,87785\,83643\,13833\,63082\,92860\,26876\,16404\,90301\,86586\,84601\,14297\,12735\,30258\,70048\,14928\,48531\,73829\,14024\,06311\,83234\,17175\,44939\,46940\,41152\,92280\,86386\,01302\,03266\,27326\,21909\,76570\,49618\,63308\,95137\,95764\,34546\,80357\,75708\,80037\,93296\,12336\,36810\,27961\,59774\,45266\,65132\,54033\,75040\,74489\,48009\,90942\,56848\,07659\,68383\,35967\,70933\,52040\,80381\,55573\,47700\,37692\,02500\,06863\,52404\,37988\,77704\,23180\,98615\,20752\,95353\,34633\,63843\,41680\,78348\,52078\,51762\,11357\,00131\,94713\,35220\,24707\,00706\,28974\,83750\,18314\,87412\,86844\,40723\,36317\,57279\,82546\,32211\,25564\,09234\,29646\,22683\,59679\,03323\,28699\,53912\,10829\,26830\,48760\,68111\,21683\,19258\,99218\,70349\,66754\,81360\,40820\,22897\,86471\,02002\,12068\,39205\,73782\,19295\,87774\,51918\,99048\,17485\,28930\,39585\,12562\,30478\,62921\,98207\,72008\,67508\,81479\,25453\,73446\,27126\,32661\,97991\,68830\,80202\,26900\,76430\,53598\,94928\,77457\,07808\,57513\,12719\,24911\,72163\,62243\,27283\,26674\,43750\,11917\,54631\,94899\,14640\,45209\,58978\,24230\,59335\,48737\,71864\,37474\,44933\,32645\,58433\,93005\,38420\,57136\,16862\,89018\,81741\,03656\,17324\,22677\,32900\,92100\,12302\,25975\,24070\,41343\,76388\,26140\,60099\,97828\,02207\,98709\,85481\,65552\,66709\,53566\,60960\,31356\,80732\,28375\,02280\,64868\,41153\,77770\,53712\,01741\,25186\,20598\,48032\,62665\,98141\,77324\,27003\,77846\,08216\,19438\,75510\,90089\,89757\,66580\,01414\,04325\,96682\,33639\,20229\,88424\,09606\,94180\,33137\,88219\,30637\,67795\,24131\,16794\,78910\,67252\,18603\,55019\,07307\,02220\,17290\,29565\,48135\,65150\,74337\,07616\,46466\,93752\,48512\,10403\,89657\,53336\,27313\,61097\,71043\,92669\,09136\,38570\,23660\,11942\,14163\,85559\,55870\,18646\,21859\,88430\,02668\,86350\,06505\,50118\,05130\,84814\,19386\,13667\,09805\,64974\,20083\,89414\,39247\,61146\,21741\,98810\,08454\,63772\,20843\,25959\,24621\,40058\,30298\,81325\,02845\,77349\,63268\,47586\,75928\,13779\,23008\,43617\,00591\,50587\,69829\,26610\,45677\,83529\,67797\,52431\,07008\,93893\,42399\,22132\,56280\,24980\,37265\,01189\,70264\,16280\,44665\,12484\,20622\,69625\,24988\,39363\,43619\,87444\,65131\,17120\,93027\,30622\,68713\,92765\,78980\,87941\,11361\,43043\,82663\,75769\,77188\,05075\,56068\,66796\,90775\,99954\,64583\,25632\,66871\,22618\,58895\,92337\,78606\,51663\,62104\,01230\,26571\,65288\,53186\,71902\,26861\,88729\,63042\,15100\,99361\,82496\,56609\,02271\,53036\,81367\,78573\,00183\,32580\,94878\,34474\,88857\,37613\,60131\,09554\,06862\,94794\,33189\,33735\,95243\,75068\,98513\,43005\,63432\,91964\,54031\,70846\,31286\,27283\,02999\,90285\,15562\,82713\,07735\,47201\,93652\,45903\,19819\,26712\,74583\,27371\,40202\,24088\,69951\,26352\,31789\,41987\,83076\,51637\,89142\,36861\,25837\,47906\,61096\,94919\,89928\,81171\,16440\,72381\,41540\,57236\,08644\,91926\,32939\,51856\,95195\,27054\,19061\,18429\,50635\,94201\,36141\,53301\,90938\,41031\,11168\,44800\,17834\,56652\,09130\,50342\,15452\,75239\,89230\,76646\,93669\,19668\,22593\,16336\,61376\,55879\,49342\,08803\,92192\,21200\,77927\,48195\,04702\,26174\,43237\,57008\,77505\,72879\,57295\,87272\,57194\,19141\,75091\,86078\,78684\,34747\,29300\,99767\,53512\,99342\,58700\,21409\,14927\,22075\,22147\,93985\,36984\,74128\,39389\,59281\,04329\,86392\,18784\,48010\,55473\,60815\,16018\,84215\,87743\,78269\,74364\,15385\,16578\,23662\,73532\,68739\,06286\,48614\,50945\,13093\,01954\,68869\,24680\,14472\,27023\,12574\,92304\,87484\,36959\,98854\,38868\,63042\,53406\,76063\,78939\,41947\,03896\,97479\,69614\,60990\,17014\,75153\,35258\,29465\,46105\,33380\,76875\,75338\,59544\,68021\,55335\,99305\,54351\,90417\,86902\,41151\,19014\,08855\,50536\,08508\,85502\,97350\,28252\,89460\,78246\,76402\,15131\,91085\,71208\,22442\,34918\,97298\,52548\,29302\,84266\,55019\,45040\,23494\,32932\,00846\,13472\,49216\,47509\,78789\,61087\,78427\,50218\,69552\,36070\,73618\,31446\,84220\,03562\,69332\,22080\,64632\,70140\,70101\,24042\,44040\,86485\,78016\,63951\,42323\,63466\,68392\,36371\,87263\,62462\,29516\,74469\,95209\,81254\,08490\,65856\,34495\,34172\,40795\,54663\,78294\,44415\,21731\,12561\,87789\,03250\,59908\,28885\,96618\,26813\,74941\,27864\,71174\,69553\,26500\,62730\,78799\,95522\,88988\,81468\,03357\,74728\,91438\,56891\,53684\,00434\,46465\,95154\,50143\,33877\,19394\,82406\,14943\,18795\,44508\,09209\,71106\,27010\,31552\,77737\,51815\,64094\,45049\,38380\,99916.

    Daniel.

    P.S.Use a 10-digit tool.As you saw "n=10000" gave 4 decimals.
     
  6. Mar 1, 2005 #5
    damn it.. i tried quite a few combinations for n upto 350000.49999 but to no avail..

    what 10 digit tool are you talking about?

    thanks
     
  7. Mar 1, 2005 #6

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    A pocket calculator,u know that small thing which has scientific functions and approximates everything to 10 digits...I don't have one with me here,but i remember that it was useful with these calculations...

    Daniel.
     
  8. Mar 1, 2005 #7
    HOLY CRAP DUDE!! :bugeye: :eek:
     
  9. Mar 2, 2005 #8

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Why did u have to quote...?Wasn't it obvious what u were referring to...?And besides,you could have quoted only a part of it...

    Yes,that Maple is quite a guy,huh...?

    Daniel.
     
  10. Mar 2, 2005 #9
    I thought the redundancy of it would be funny I guess
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Log Help
  1. Help with natural logs (Replies: 8)

Loading...