Tagged Questions

Questions related to real and complex logarithms.

35 views

Proving logarithmic maths graphically

I'm just going through some further maths units as I prepare for a PHD in chemical engineering. I'm finding the thought processes to be invaluable in my problem solving skills. However, I recently ...
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Finding x and y from two given logarithmic equations

I'm just studying some further mathematics units for my own benefit before I undertake a PHD in chemical engineering next year. I feel the learning of the mathematical concepts at this level will help ...
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Need to overcome erroneous result when differentiating natural log of a fraction

I am trying to differentiate the following: $$ln(3x-8/6x+2)$$ my (incorrect) method is: let $$ln(x) = ln(u)$$ therefore when differentiating u.. $$ln(u) = 1/u$$ and diff of(3x-8/6x+2) = 3/6 = 0....
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Evaluate $\lim_{x\rightarrow\infty} \ln(x^2+1)-\ln(x-1)$

How would you solve the following limit? The method I used can be seen below. I'm just not sure if it's valid. I was thinking perhaps a substitution for $(x-1)$ might also work, but when I followed ...
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Prove that $f(ab) = f(a) + f(b)$

Question : Assume only that $f: (0,\infty)\to{\mathbb{R}}$ is differentiable and that $f'(x) = 1/x$, and $f(1)=0$. Prove that for all $a,b \in(0,\infty)$, $f(ab)=f(a)+f(b)$. [Hint: Let $g(x)=f(ax)$] ...
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Formula for calculating markup with big % for small amounts and small % for larger amounts

I am trying to come up with a formula for calculating markup for products that range in value from a few cents up to tens of Dollars. At 10c I would like the markup to be around 500%, and from 2 ...
258 views

Proving $x$ is a given quotient of logarithms

I'm practicing some questions on logarithms at the moment in order that I'm up to speed with the problem solving aspect before I embark on my PHD in chemical engineering at Boston college next year. ...
42 views

Natural Logs and Anit-Derivatives are kicking me

I am given a problem involving rates of flow, $F(t)=\frac{t+7}{2+t}$ is the rate at which a bucket is being filled. The same bucket is being emptied at a rate given by $E(t)=\frac{\ln(t+4)}{t+2}$. My ...
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Exhaustive search times: 2 to power k = 100 hours - double k, how many hours

An exhaustive search (i.e. checking all combinations of values) takes 100 hours to go through all permutations where a binary key has a length of k. $2^k$ = 100 hours where k is the number of digits ...
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log(x,2log(2x, 2log(2,4x))) >1 , find answers of x

how i slove it , please help me? log(x,2log(2x, 2log(2,4x))) >1 my try: if x>1 =>2log(2x, 2log(2,4x))>x => 2log(2,4x)>(2x)^(x/2) =>4x>2^(((2x)^(x/2))/2) another way log(x,2log(2x, 2log(2,4x)))=...
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If $\log_35=a$ and $\log_54=b$, what is $\log_{60}70$?

One student sent me this question: If $\log_35=a$ and $\log_54=b$, what is $\log_{60}70$? Question asks the value of $\log_{60}70$ in terms of $a$ and $b$. Equations for $a$ and $b$ involved $2$,...
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Multiplying two logarithms (Solved)

I was wondering how one would multiply two logarithms together? Say, for example, that I had: $$\log x·\log 2x < 0$$ How would one solve this? And if it weren't possible, what would its domain ...
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Cancelling a logarithm

I was wondering if there was a way to cancel out a logarithm? For example: $\log_a A$ > $\log_a B$ What would a have to be for the log to go away and be left with A > B? Thanks in advance!
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So many logs with different bases

$\large { 6 }^{ \log _{ 5 }{ x } }\log _{ 3 }( { x }^{ 5 } ) -{ 5 }^{ \log _{ 6 }{ 6x } }\log _{ 3 }{ \frac { x }{ 3 } } ={ 6 }^{ \log _{ 5 }{ 5x } }-{ 5 }^{ \log _{ 6 }{ x } }$ The sum of the ...
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Find unknown x coordinate from log graph

I am not sure where to start on this question. I am not sure how to fit the coordinates into the equation $y=\log_3(x-4)$
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How do you solve $x^2 = \left(\frac 12\right)^x$?

I'm having trouble finding the steps to solve for $x$. The solutions to this equation are $x=-4$, $x=-2$, and $x=0.76666$ when solved graphically and through the solve function of a TI-nspire cx CAS. ...
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How to prove derivative of logarithm with base $b$?

I learned how to derive a logarithm with any base. This is the formula: $$\frac{d}{dx}\log_bx=\frac{1}{x\ln b}$$ How can it be proved?