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Math Help - log 0.001^x

  1. #1
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    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!
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by hydride View Post
    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
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  3. #3
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    Thanks for the fast reply!
    But can you explain the steps?
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  4. #4
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    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

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  5. #5
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    Thank you!
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