1. ## log 0.001^x

$log 0.001^x$

how do you solve it?

I know its still base 10, but that variable exponent throws me off. What is the equation equal to too? Is it y?

I think in number form it is $10^y = 0.001^x$...is it?

Thanks!

2. Originally Posted by hydride
$log 0.001^x$

how do you solve it?

I know its still base 10, but that variable exponent throws me off. What is the equation equal to too? Is it y?

I think in number form it is $10^y = 0.001^x$...is it?

Thanks!
$log_{10}(0.001^x) = x\,log_{10}(0.001) = -3x$

3. Thanks for the fast reply!
But can you explain the steps?

4. Hello, hydride!

$\text{Simplify: }\;\log\left(0.001^x\right)$

$\log\left(\frac{1}{1000}\right)^x \;=\;\log\left(\frac{1}{10^3}\right)^x \;=\;\log\left(10^{-3}\right)^x \;=\;\log\left(10^{-3x}\right) \;=\;-3x\underbrace{\log(10)}_{\text{This is 1}} \;=\;-3x$

5. Thank you!