# Math Help - Find dy/dx

1. ## Find dy/dx

$y=\log{(6x)}$

2. Originally Posted by Jim Marnell
$y=\log{(6x)}$
This depends on if you mean $\log_{10}(x)$ or $\log_{e}(x)=\ln(x)$

3. I assume by log(6x) you are referring to the base 10 logarithm

y = log(6x) = log(6) +log(x) = log(6) +ln(x)/ln(10)

dy/dx = 1/[xln(10]

4. U need to define a base for this log (6x) ..... for example

$log_{\alpha}(6x)$

After this u will have:

$y=log_{\alpha}(6x)=\frac{ln(6x)}{ln(\alpha)}$

$\Rightarrow dy=\frac{1}{6xln(\alpha)}*(6x)' dx$

$\Rightarrow dy=\frac{1}{6xln(\alpha)}*6 dx$

$\Rightarrow dy=\frac{1}{xln(\alpha)} dx$

$\Rightarrow dy=\frac{1}{xln(\alpha)} dx$

$\Rightarrow \frac{dy}{dx}=\frac{1}{xln(\alpha)}$

Have a nice day

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