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I'm lost on how to solve this for z. Can anyone help?

$\left(7^\left(-2z\right)\right)^\left(7-z\right) = 49^\left(-12\right)$

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3 Answers 3

up vote 5 down vote accepted

The equation is equivalent to $7^{(-2x)(7-x)}=7^{2\cdot(-12)}$.

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Take $\log_{7}$ of both sides and then simplify.

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Write $7^{-2z}$ as $(7^2)^{-z} = 49^{-z}$

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