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Thread: Exponential into logarithm equation

  1. #1
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    Question Exponential into logarithm equation

    Hi,

    I hope someone can help. I'm trying to convert y=100(2)^(x/0.32) to its inverse in logarithmic form. However, I'm struggling with the conversion steps.

    Can someone show me step-by-step on how to convert this equation? The answer is y = 0.32log(base 2)(x/100)

    Thanks,
    Olivia
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  2. #2
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    Re: Exponential into logarithm equation

    y=100(2)^(x/0.32)
    $y = 100 \cdot 2^{x/0.32}$

    $\dfrac{y}{100} = 2^{x/0.32}$

    $\log_2\left(\dfrac{y}{100}\right) = \log_2\left(2^{x/0.32}\right)$

    $\log_2\left(\dfrac{y}{100}\right) = \dfrac{x}{0.32}$

    $0.32 \cdot \log_2\left(\dfrac{y}{100}\right) = x$

    swap $x$ and $y$ ...
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  3. #3
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    Re: Exponential into logarithm equation

    Makes sense. Thank you very much
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