# Thread: integrate logarithm with base 10

1. ## integrate logarithm with base 10

I don't know how to make the symbols yet so if you don't understand what the problem is feel free to say it, I can't seem to get a hold on integrating log quotients.
The Problem: Indefinite integral of (log10(x))/x dx --> log (base 10)x divided by x --> seems really easy, i just don't know why I can't figure it out. I tried by parts but I got confused thinking that I can't use that method for quotients, I'm not even sure if that's true if not please tell me.

2. Originally Posted by bgonzal8
I don't know how to make the symbols yet so if you don't understand what the problem is feel free to say it, I can't seem to get a hold on integrating log quotients.
The Problem: Indefinite integral of (log10(x))/x dx --> log (base 10)x divided by x --> seems really easy, i just don't know why I can't figure it out. I tried by parts but I got confused thinking that I can't use that method for quotients, I'm not even sure if that's true if not please tell me.
note ... $\displaystyle \log_{10}x = \frac{\ln{x}}{\ln(10)}$

$\displaystyle \frac{1}{\ln(10)} \int \frac{\ln{x}}{x} \, dx$

method of substitution ...

let $\displaystyle u = \ln{x}$ ... $\displaystyle du = \frac{1}{x} \, dx$

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# integral of log base 10 x

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