# Thread: Exponential into logarithm equation

1. ## 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

2. ## 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 $y$ ...

3. ## Re: Exponential into logarithm equation

Makes sense. Thank you very much