How do you solve the exponential equation $3^(x-7)=27^(2x)$ ?

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Answer 1 · 2017-02-19T00:29:12

$x=-7/5$

Rewrite the right hand side as follows

$3^(x-7)=(3^3)^(2x)$

Using the property $(a^y)^x=a^(yx)$

We can further rewrite the right side

$3^(x-7)=3^(6x)$

Since we now have both sides in terms of the same base

$x-7=6x$

$-5x=7$

$x=-7/5$

How do you solve the exponential equation 3^(x-7)=27^(2x)3^(x-7)=27^(2x)?