# Tagged Questions

Questions related to real and complex logarithms.

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### How to solve $3(a+1)(b+1)=3^a \times 2^b$?

Hi I'm new to logarithms and not sure how to solve equations involving logarithms. I managed to find this equation to answer a problem solving question, however now I do not know how to solve the ...
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### Solve the following equation : $\log_2(x)*\log_4(x)*\log_8(x)=4.5$

I have the following equation : $$\log_2(x)*\log_4(x)*\log_8(x)=4.5$$ Usually, I do post what I made to do, but in this case a friend of mine tackle me with this question after I didn't mess with ...
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### Is the value of $\log_27$ a rational number?

Is $\log_27$ a rational number?
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### Use the definition of $\ln(x)$ as an integral to show that $f(x)=\frac{ln(x)}{x^2} \leq 1/x$ for all $x\geq 1$.

As the title says, if we let $$f(x)=\frac{ln(x)}{x^2}$$ I know that $$ln(x)=\int_1^x \frac{dt}{t} dt$$ Since $x^2 >0$ we can rewrite the question as $ln(x) \lt x$ $\forall$ $x\ge1$ How do we ...
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### Logarithmic Taylor series question [closed]

Consider the transformation of variables, x = $\frac{y+1}{y-1}$ How would you develop log(x) as a Taylor Series in y about zero?
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### How to show that: $\log_a (x^{a}-x)-\log_a \Big(\dfrac{x^{a}-x}{a}\Big)=1$, where $a$ and $x$ are positive integers.

I was studying Fermat's Little Theorem and Logarithm to see if there is any interesting result or correlation exist between the two. So I came up with this equation. I know few basic logarithmic ...
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### Proof without words for logarithmic funtions [closed]

I'm looking for a PROOF WITHOUT words for logarithms. The only one I've seen is calculus based and I need one for a younger audience. Any help/suggestions would be appreciated! This is the example I ...
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### forming log equation from graph points

Okay so I need to form a logarithmic equation from the points (1960,4.7) (1964,5.1) (1968,5.4). I have 'guess and checked' to get the equation 2.7421 log(x-1950)+1.9579, and was wondering if there was ...
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### Solve logarithm without calculator for exam practice [closed]

How to solve $$\log_{3}(x)+\log_{3}(3x) = 3$$ ?
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### Why do these “equal” logarithms give different answers

This came across a discussion amongst Algebra 2 teachers at my school. We know $a\log x= \log x^a$ Say $2\log x=5$ $\log x^2 =5$ When $\log x=\log_{10} x$ Solving the first equation yields $x=10^{5/2}$...
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### Finding the value of x, logarithms and exponentials

I'm working through some logs and exponentials questions at the moment in order so that I might be a little prepared for any I might utilize in a science PHD. I'm currently getting through the ...
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### What is the difference in this question between $\log$ and $\lg$?

Am I right in assuming that $\lg$ just refers to $\log$ base ($10$)? Whereas $\log$ is just any unspecified log? I'm solving $\lg{15}-\lg{5}$ Am I good to just use the standard rules of logarithms, ...
### Integral involving logarithm: $\int_0^\infty \frac{ \ln x}{(x+a)(x+b)} dx$
How to solve the following integral $$\int_{0}^{\infty} \frac{ \ln x}{(x+a)(x+b)} dx,$$ where $a,b>0$ and $a \neq b$. I was looking for some kind of substitution. However, I don't see an obvious ...