Logarithms Definition and 255 Threads

hints? Derivatives: Intervals, stationary points, logarithms, continuous functions Homework Statement Got any hints or anything? 1. Suppose that f(x) = (x - 3)^4 ( 2x + 5)^5 a) Find and simplify f ' ( x ) b) Find stationary points of f c) Find exactly the intervals where f is...

Does anyone know how to proof the following: a^(log(b))=b^(log(a)) for a,b>0

logarithms STUCK! 8logx-3logx^2 = log8x - log4x im struggling to find x. my working out so far is: rhs log8x-log4x = log2 = 8logx - 3logx^2 = log 2 = 8logx - 3logx^2 - log 2 = 0 = -b+ or - the square root of b^2-4ac divided by 2a a = -3 b = 8 c = - 2 = -8 + or - sqaure...

Homework Statement If tan-1z = (1/2i)ln[(1+iz)/(1-iz)] then find tan-1[(2sqrt(3) - 3i)/7] The Attempt at a Solution I haven't gotten very far, but this is what I have so far: tan-1[(2sqrt(3) - 3i)/7] = (1/2i)ln[(i2sqrt(3) + 10)/(i2sqrt(3) + 4)] Where do you go...

I have 2lnx = xln2 where x\ne2 if you start by dividing both sides by ln2 is the following legal? \frac{2lnx}{ln2} \rightarrow x = 2ln(x-2) e^{2ln(x-2)} = (x-2)^2 x = (x-2)^2 \implies x = 4

I read that \log _2 (3) = {\ln (3) \over \ln (2)} Is \log _a (b) = {\ln (b) \over \ln (a)} How?

Hi, I missed a few days of my calculus class. I've managed to figure out how to use substitution to solve an indefinite integral, and can apply the log properties to some extent. I just can't figure out this problem. Homework Statement Find the indefinite integral: \int{\frac{1}{x...

Homework Statement Using integration by parts, integrate: (1/x^2)(lnx) dx with the limits e and 1 Homework Equations [uv]to the limits a b - the integral of (v)(du/dx) dx (sorry, don't know how to write out equations properly on a computer) The Attempt at a Solution I've...

Hello I was wondering if someone could help me. I've got a question on evaluating logarithms, but I've not done anything like this before. I'm only used to the basic logarithmic stuff, and I still find that a bit confusing. So, I've been trying to do this question for hours now, and...

The integral of ln(1-x) is -(1-x)ln(1-x)-x, when 0<=x<=1. So for example: \int_{0}^{1} ln (1-x)dx= (-(1-x)ln(1-x)+x)_{0}^{1}=-1 However, going to an online integrating site: http://integrals.wolfram.com/index.jsp?expr=Log[1-x]&random=false they give the integral of ln(1-x) as...

I was just wondering what's the "magic" behind logarithms. Just took them in school, and I get the part that they're just the reverse of exponents but it still feels sort of like a mystery every time I solve a logarithm using a calculator. Just like how addition is the slow way of...

Homework Statement lnx+ ln(x-1) = 1 solve each equation for x Homework Equations ln(e^x) = x e^lnx = x The Attempt at a Solution x + (x-1) = e^1 [==> using ln(e^x) = x] from this point on, I am stuck because I am having trouble isolating x because of the x that is in the brackets...

Is it possible to make a formula for logarithms of any base? logb(a)=x I want to find x through some formula. I've seen that you can use a series for e as the base, is that the only base that can be solved for? Is there any work being done to accomplish this, or, maybe it has been...

1. ln (x2 / y2) = log (A / B) = logA-logB = logx2-logy2 = 2logx - 2logy (is this correct) 2. can this expression be split into separate log functions and numbers, is this question the answer log(2x + 3y) = log(2x + 3y) (is this correct)

it is suspected that cells in a sample are dividing so that the number of cells present at anyone time t (measured in seconds) is growing exponentially according to the relationship y = 64 x 2^2t. it would be hard to check this relationship accurately by plotting measurements of y against t, so...

I know why I can add 2 \pi i to log_{e} \omega ( log_{e} \omega = log_{e}z + i \theta if \omega = z(cos \theta +i sen \theta ) ) but I can't understand why I can add \frac{2 \pi i}{log_{e}b} to log_{b} \omega . Does anyone have the answer for me? Thanks!

Homework Statement log(1/2xy^2) = ln x + 3 ln y - ln 2 Homework Equations The Attempt at a Solution i have been trying for hours on with next to no results even just an insight on how to go about it would be helpful

I'm reading book called "Prime Obession" which attempts to give a layperson's introduction to the Riemann Hypothesis. In laying the groundwork in one of the early chapters the author is explaining the fact that the function log(x) increases more slowly in total than x raised to any power. For...

Homework Statement Put in Exponential form and solve for X. SHOW YOUR STEPS! log2(x-5)=5 Homework Equations I am not sure what this is asking for. There are no other equations. The Attempt at a Solution 25=X-5 25+5=X-5+5 32+5=X X=37

Homework Statement Calculate the sum of the following series: \sum_{i=2}^{\infty}(-1)^i \cdot \lg ^{(i)} n Where (i) as a super-script signifies number of times lg was operated i.e. \lg ^{(3)} n = (\lg (\lg (\lg n))) , and n is a natural number. Homework Equations The Attempt...

ln(x+1) + ln(x+3) < ln(x+7) Find x! I should of course know this, second year at high school (in Norway). I've just forgotten the way attack the whole thing^^

Is there a way to quickly calculate a log by hand? It needs to be "quick & dirty", much like other arithmetic done by hand (i.e. it doesn't have to be pretty, but needs to be quick and accurate, or at the very least, a very accurate estimate). The only thing I can think of is trial & error...

Homework Statement Solve for x. State restrictions, if necessary. 3^(2x) - 3^(x) -12 = 0 Homework Equations The Attempt at a Solution 2xlog3 - log3 = log 12 x=log 12/log 3 Doesn't work. I have no idea how to do this.. we didn't learn it. The 2x is throwing me off.

Homework Statement 12^x=4X8^(2x) Big X= multiplication sign little x= unknown i simply cannot figure this out. Any help please? Homework Equations 4.6X1.06^(2x+3)=5X3^(x)

I encountered a proof problem when I was reading up on the derivatives of natural logarithms' section. It gave a rule which said this : \text{For } a >0 \text{ and } a\ne 1 \text{,}\\\frac{d}{dx}(a^{u}) \ = \ a^{u} \ \ln{a\frac{du}{dx}} To prove it on my own, I made a few identities: a^{u}=y...

Hi! I'm having trouble solving this limit: lim x->infinite ln(1+2^x)ln(1+3/x) Revelation

Homework Statement Im not looking for answers as i know the answers already. i also know that given time and a calculator, i could figure these out, but i have neither for the exams. I am just wondering the general way of setting problems like this up, so i can solve others in the future...

I have to prove that 2^n > n^2 for every n>=5 So... 2^k > k^2 /log base 2 log2(2^k) > log2(k^2) k*log2(2) > 2*log2(k) k/2 > log2(k) So I'm stuck here and I am having problems solving for k, since i have it on both sides. I just need someone to gimme a slight push :)

I have two problems if that's ok with you 1. log((x-3)/(x+3)) <= 1 2. 6*9^(1/x) - 13*6^(1/x) + 6*4^(1/x) = 0 So for the first one i didnt get too far. I divided the logarithm and i got: log(x-3) + log(x+3) <= 1 For the second one i used logarithms and received: log6 + 1/x*log9...

Solve the equation log2x + log4x= 5. To start, should I change this to an exponential... I am stuck because I have only done log questions that have the same base.

Fix b >1, \ y >0 , and prove that there is a unique real x such that b^{x} = y . Here is the outline: (a) For any positive integer n , b^{n}-1 \geq n(b-1) . Why do we do this? (b) So b-1 > n(b^{1/n}-1) . (c) If t>1 and n > (b-1)/(t-1) then b^{1/n} < t . etc.. Is...

I have these questions that are due tomorrow I am completely clueless on what my teacher is asking. 1. What is log(x), Explain. I think that is like a parent function not sure 2.What is 10^log(10) I know that it graphs as a straight line but that's it...

Logarithms and Intensity---HELP ASAP! Homework Statement a)What is the intensity of sound at 123 dB? b)Compare it to that of a whisper at 20 dB. Homework Equations something with logarithms?? The Attempt at a Solution a) 10^123

4^{sinx} = \sqrt[cosx]{2} I use logarithmic and i get : sinx * log(4) = (1/cosx) * log(2) sinx*cosx = log(2)/log(4) what should i do next?

what are common logarithms? my textbook doesn't explain it very well

Homework Statement Find the real & imaginary parts of log(1+i)log(i) ? Homework Equations The Attempt at a Solution

do Logarithms play any major part in being able to do calculus?

[SOLVED] derivative with logarithms Ok, so the problem problem probably isn't as bad as I'm making it, either that or its because its getting late & my brain just isn't functioning. Find the derivative of y with respect to r. y=log _2 \left( r \right) * log _4 \left( r \right) The...

Evaluate the integral. \int3/(3x-2) dx from 0 to -1 (top to bottom). I change the equation to [tex(1/x - 3/2) dx[/tex] then integrated ln x-3/2x, but ln x at 0 is undefined. The textbook shows it as becoming ln (3x-2), but I'm not completely understanding how to get to that.

Just a quick check, I've spend hours trying to crack this. Have I gone the right way about it? Homework Statement Solve 5^(x-1)= 4^(1-3x) Homework Equations The Attempt at a Solution (x-1)log5 = log4 (1-3x) xlog5 - log5 = log4 - 3xlog4 xlog5 + 3xlog4= log4 + log 5...

[SOLVED] Logarithms and Exponents Question Homework Statement 5^{x}=41 The attempt at a solution Well, I know that one way to figure this out would be that to find a common base for both sides of the equation and then use the known exponent to find the variable. The only thing...

1. Differenciate the following functions i) y = x2ln(4x) ii) y = ln (x + 1)/x iii) y = ln (x2 - 1)1/22. Laws for differentiating logs and exponentials 3. I did some of the more easy one's, these ones just got me stumped. i) i think you would use the product rule. so u = x2 and v =...

Question: A new disinfectant spray is expected to kill 50% of the known germs in a room, but for health reasons it can only be used once a day. Between spraying, the germs increase by 25%. How many consecutive days of spraying are required to reduce the germs in the room to 10% of the original...

All information, including the problem, is attached. So far I think I've proven by induction that log (a^r) = r log (a) whenever r is an integer, but I need to prove this for all rational numbers r = p/q . We're working with the functional equation that has the property that f(xy) = f(x)...

Homework Statement ln(x^2 + 1 ) -3lnx=ln2 Solve for x. Homework Equations The Attempt at a Solution I used laws of logarithms to simplify it down to -x^2(x-1)=1 . I don't think this is the answer I'm under the impression you need x = for the answer. First I brought the 3...

I've been working on logarithms in my calculus class and I came acrossed one with a square root. Since I am new to these types of problems I'm not sure how to work with this yet. How would I solve something such as loge[square root of e]

Homework Statement 3^(x - 2) = 30 (x - 2)^3 = 30 log (base 4) (x + 3) + log (base 4) (x - 3) = 2 the square root of: (4^(x + 3) / 16^x) = 32 log (base 9) x = 1.5 Homework Equations NONE The Attempt at a Solution I haven't done this since last year. Someone refresh my...

Homework Statement #8: Simplify: log[SIZE="1"]91/27 Homework Equations y=log[SIZE="1"]b(x) x=b^y The Attempt at a Solution I have personally not tried logarithms before, but I think the problem is really easy and I am probably just over-thinking it? I think that, using the formula's below...

Homework Statement Express b^{x} as a function of logarithms. Homework Equations There are a couple of equations in the attempted solution. I can't say if they are actually relevant The Attempt at a Solution I've investigated the property y = log_{b}(b^{y}), and also...

Hi I really need ur help I was sick in the days that the teacher gave us the lesson and I really really need ur help this is the equation : 2 log{to base x} of 5 + log{to base 5} of x = log 1000 i know that log 1000 = 3 and 2 log{to base x} of 5 = log{to base...