- #1
scilover89
- 78
- 0
Even calculator can't solve this...
(8^2003+6^2003)/49=?
Who can solve this?
(8^2003+6^2003)/49=?
Who can solve this?
Can Modern Calculators Solve (8^2003 + 6^2003) / 49?
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SUMMARY
The discussion centers on the mathematical expression (8^2003 + 6^2003) / 49 and its solvability using modern calculators. The calculations reveal that 8^2003 approximates to 7.75 * 10^1808, while 6^2003 is significantly smaller at approximately 4.335 * 10^1558, allowing for simplification. The final result, calculated using Mathematica, is approximately 1.5814223227342232267895223637314066 * 10^1807, with a detailed decimal expansion provided. The exact answer is a lengthy integer followed by a fraction of 2/7.
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- #2
Gokul43201
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8^{2003} = 10^{2003*log_{10}8} = 10^{1808.88924} = 7.75 * 10^{1808}
6^{2003} = 10^{2003*log_{10}6} = 10^{1558.63695} = 4.335 * 10^{1558}
The second can be neglected in comparison to the first giving
(8^{2003}+6^{2003})/49 = (about)~ 1.5816 * 10^{1807}
Also, if you wrote out the full number (in decimal expansion) in all its gory detail, the digits after the decimal point would be .04081632653... for whatever that's worth.
6^{2003} = 10^{2003*log_{10}6} = 10^{1558.63695} = 4.335 * 10^{1558}
The second can be neglected in comparison to the first giving
(8^{2003}+6^{2003})/49 = (about)~ 1.5816 * 10^{1807}
Also, if you wrote out the full number (in decimal expansion) in all its gory detail, the digits after the decimal point would be .04081632653... for whatever that's worth.
Last edited:
- #3
houserichichi
- 40
- 0
Well, I didn't do the arithmetic, but the answer is
110699562591395625875266564924664097310974709512929097789175911617601046454386434533363625521484979625995866415556215005295416133194216915274253564533823808741077943952672510750053902252973351456954446065237629947590350789140326338000369452446840290082144467142045178897824353048670587312080224265459784206322855624222209627723142215253195344567886035909787077726154777006320959340849530325395879878645900740268181333554850414711304850535157904078675787256343935250506945484632580361260539052711292135393964305721326164034185323257036401562064939229517300512382832378049844366899876452596800955806420515203883818227428415114965787363900634482730394595855901269536477229409114070793987701830131336961091311521917948013656268286590558122942173068042452683584041597393131362115133639708695813827166004500777279577036282790847755599032408449092996078742277433061567299573578686181516485959696804800782360503486653196727233559342142902572693633989299389429306974042715177724597042437294815094190562672889102497380940799682008786172658233122667320788812823727542218978920706958595020667644482284910188722257885885010942161301492075556745333658141372608295823959953020682907150950904979738403629013487885794876482903052545000231653116968614767872331012877153046697429893686056710998765089687784315909815005258973458134465324287048736599893117632184261219444205283823063443143881361385024937369090408673392508695811724593424721886293429928788520837043197212862355297138917320309016807737396766789530004574754173260914474719164345351785481277844433138044222960404781867964113414476335964916396492692453035888217537736329111435482807135250055792650863889863243772287640514370785654038798197610745561837609318531738132668887103225077809387770418238590052166821081931085756853573798577748014227700555866270649651879215104
divided by 7, which can be shortened to approximately
1.5814223227342232267895223637314066 * 10^1807
Mathematica did it, not me
Excuse the strange spacing too...it's late and I feel no urge to write simple latex.
110699562591395625875266564924664097310974709512929097789175911617601046454386434533363625521484979625995866415556215005295416133194216915274253564533823808741077943952672510750053902252973351456954446065237629947590350789140326338000369452446840290082144467142045178897824353048670587312080224265459784206322855624222209627723142215253195344567886035909787077726154777006320959340849530325395879878645900740268181333554850414711304850535157904078675787256343935250506945484632580361260539052711292135393964305721326164034185323257036401562064939229517300512382832378049844366899876452596800955806420515203883818227428415114965787363900634482730394595855901269536477229409114070793987701830131336961091311521917948013656268286590558122942173068042452683584041597393131362115133639708695813827166004500777279577036282790847755599032408449092996078742277433061567299573578686181516485959696804800782360503486653196727233559342142902572693633989299389429306974042715177724597042437294815094190562672889102497380940799682008786172658233122667320788812823727542218978920706958595020667644482284910188722257885885010942161301492075556745333658141372608295823959953020682907150950904979738403629013487885794876482903052545000231653116968614767872331012877153046697429893686056710998765089687784315909815005258973458134465324287048736599893117632184261219444205283823063443143881361385024937369090408673392508695811724593424721886293429928788520837043197212862355297138917320309016807737396766789530004574754173260914474719164345351785481277844433138044222960404781867964113414476335964916396492692453035888217537736329111435482807135250055792650863889863243772287640514370785654038798197610745561837609318531738132668887103225077809387770418238590052166821081931085756853573798577748014227700555866270649651879215104
divided by 7, which can be shortened to approximately
1.5814223227342232267895223637314066 * 10^1807
Mathematica did it, not me
Excuse the strange spacing too...it's late and I feel no urge to write simple latex.
Last edited:
- #4
Zurtex
Science Advisor
Homework Helper
- 1,118
- 1
The exact answer is:
15814223227342232267895223560666299615853529930418442541310844516800149493483776361909089360212139946570838059365173572185059447599173845039179080647689115534439706278953215821436271750424764493850635152176804278227192969877189476857195636063834327154592066734577882699689193292667226758868603466494254886617550803460315661103306030750456477795412290844255296818022111000902994191549932903627982839806557248609740190507835773530186407219308272011239398179477705035786706497804654337322934150387327447913423472245903737719169331893862343080294991318502471501768976054007120623842839493228114422258060073600554831175346916444995112480557233497532913513693700181362353889915587724399141100261447333851584473074559706859093752612370079731848881866863207526226291656770447337445019091386956544832452286357253897082433754684406822228433201207013285154106039633294509614224796955168788069422813829257254622929069521885246747651334591843224670519141328484204186710577530739674942434633899259299170080381841300356768705828526001255167522604731809617255544689103934602711274386708370717238234926040701455531751126555001563165900213153650963619094020196086899403422850431526129592992986425676914804144783983684982354700436077857175950445281230681124618716125307578099632841955150958714109298526826330844259286465567636876352189183864105228556159661740608745634886469117580491877697337340717848195584344096198929813687389227632103126613347132684074405291885316123193613876988188615573829676770966684218572082107739037273496388452049335969354468263490448292031851486397409709159059210905137845199498956064719412602505390904158776497543876464293684664409127123320538898234359195826522005542599658677937405372759790248304666983871889296829912538631176941436023831583133012250979081971225392573461100079409467235664554173586 + 2/7
As 82003+62003 is:
774896938139769381126865954472648681176822966590503684524231381323207325180705041733545378650394857381971064908893505037067912932359518406919774951736766661187545607668707575250377315770813460198681122456663409633132455523982284366002586167127882030575011269994316252284770471340694111184561569858218489444259989369555467394061995506772367411975202251368509544083083439044246715385946712277771159150521305181877269334883952902979133953746105328550730510794407546753548618392428062528823773368979044947757750140049283148239297262799254810934454574606621103586679826646348910568299135168177606690644943606427186727591998905804760511547304441379112762170991308886755340605863798495557913912810919358727639180653425636095593878006133906860595211476297168785088291181751919534805935477960870696790162031505440957039253979535934289193226859143650972551195942031430971097015050803270615401717877633605476523524406572377090634915395000318008855437925095726005148818299006244072179297061063705659333938710223717481666585597774061503208607631858671245521689766092795532852444948710165144673511375994371321055805201195076595129110444528897217335606989608258070767719671144780350056656334858168825403094415200564135380321367815001621571818780303375106317090140071326882009255802396976991355627814490211368705036812814206941257270009341156199251823425289828536109436986761444102007169529695174561583632860713747560870682072153973053204054009501519645859302380490036487079972421242163117654161777367526710032023279212826401323034150417462498368944911031966309560722833473075748793901334351754414775448847171251217522764154303780048379649946750390548556047229042706406013483600595499578271587383275218932863265229722166928682209722575544665714392927670130365167747573517600297975016590044236099593903891063894547563154505728
Edit my fault[/size] I misread the post, I've corrected it now
15814223227342232267895223560666299615853529930418442541310844516800149493483776361909089360212139946570838059365173572185059447599173845039179080647689115534439706278953215821436271750424764493850635152176804278227192969877189476857195636063834327154592066734577882699689193292667226758868603466494254886617550803460315661103306030750456477795412290844255296818022111000902994191549932903627982839806557248609740190507835773530186407219308272011239398179477705035786706497804654337322934150387327447913423472245903737719169331893862343080294991318502471501768976054007120623842839493228114422258060073600554831175346916444995112480557233497532913513693700181362353889915587724399141100261447333851584473074559706859093752612370079731848881866863207526226291656770447337445019091386956544832452286357253897082433754684406822228433201207013285154106039633294509614224796955168788069422813829257254622929069521885246747651334591843224670519141328484204186710577530739674942434633899259299170080381841300356768705828526001255167522604731809617255544689103934602711274386708370717238234926040701455531751126555001563165900213153650963619094020196086899403422850431526129592992986425676914804144783983684982354700436077857175950445281230681124618716125307578099632841955150958714109298526826330844259286465567636876352189183864105228556159661740608745634886469117580491877697337340717848195584344096198929813687389227632103126613347132684074405291885316123193613876988188615573829676770966684218572082107739037273496388452049335969354468263490448292031851486397409709159059210905137845199498956064719412602505390904158776497543876464293684664409127123320538898234359195826522005542599658677937405372759790248304666983871889296829912538631176941436023831583133012250979081971225392573461100079409467235664554173586 + 2/7
As 82003+62003 is:
774896938139769381126865954472648681176822966590503684524231381323207325180705041733545378650394857381971064908893505037067912932359518406919774951736766661187545607668707575250377315770813460198681122456663409633132455523982284366002586167127882030575011269994316252284770471340694111184561569858218489444259989369555467394061995506772367411975202251368509544083083439044246715385946712277771159150521305181877269334883952902979133953746105328550730510794407546753548618392428062528823773368979044947757750140049283148239297262799254810934454574606621103586679826646348910568299135168177606690644943606427186727591998905804760511547304441379112762170991308886755340605863798495557913912810919358727639180653425636095593878006133906860595211476297168785088291181751919534805935477960870696790162031505440957039253979535934289193226859143650972551195942031430971097015050803270615401717877633605476523524406572377090634915395000318008855437925095726005148818299006244072179297061063705659333938710223717481666585597774061503208607631858671245521689766092795532852444948710165144673511375994371321055805201195076595129110444528897217335606989608258070767719671144780350056656334858168825403094415200564135380321367815001621571818780303375106317090140071326882009255802396976991355627814490211368705036812814206941257270009341156199251823425289828536109436986761444102007169529695174561583632860713747560870682072153973053204054009501519645859302380490036487079972421242163117654161777367526710032023279212826401323034150417462498368944911031966309560722833473075748793901334351754414775448847171251217522764154303780048379649946750390548556047229042706406013483600595499578271587383275218932863265229722166928682209722575544665714392927670130365167747573517600297975016590044236099593903891063894547563154505728
Edit my fault[/size] I misread the post, I've corrected it now
Last edited:
- #5
FZ+
- 1,594
- 3
The question is...
Why?
Why?
- #6
NeutronStar
- 419
- 1
The answer is,...FZ+ said:
Why not?
- #7
Gokul43201
Staff Emeritus
Science Advisor
Gold Member
- 7,207
- 25
Yes, that is the question.
EDIT : DAMN, beat to the punch...and by a dissenter, at that. bah !
EDIT : DAMN, beat to the punch...and by a dissenter, at that. bah !
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