1. ## log 0.001^x

$\displaystyle log 0.001^x$

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 $\displaystyle 10^y = 0.001^x$...is it?

Thanks!

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

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 $\displaystyle 10^y = 0.001^x$...is it?

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

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

4. Hello, hydride!

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

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

5. Thank you!

,

### log 0.001=x

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