$\displaystyle log 0.001^x$

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!

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- Oct 6th 2009, 12:53 PM #1

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- Oct 6th 2009, 01:01 PM #2

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- Oct 6th 2009, 02:03 PM #4

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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 $

- Oct 6th 2009, 02:05 PM #5

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