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How would I find the inverse of $$\ln(8x-64)?$$

I've tried put $8x-64$ as the power to the base of $e$, I don't know what to do from there on, thanks in advance

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2 Answers

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Set, $y=\log(8x-64)$ and solve for x.

So , $$e^y=e^{\log(8x-64)}$$ $$e^y=8x-64$$

You should be able to go from here.

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Assuming you want to find the inverse of the function $$f(x) = \ln(8x-64)$$

You want a function $g(y)$ such that $g\left(f(x)\right) = x$, so $$g\left(\ln(8x-64)\right) =x$$

This means $y = \ln(8x-64)$, so $$e^y = 8x-64$$

$$\frac{e^y + 64}{8} = g(y)$$

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