Solve $4^(3x)=8^(x-2)$ ? Thank You.

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Solve $4^(3x)=8^(x-2)$ ? Thank You.

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Answer 1 · 2017-07-02T09:54:09

$x=-2$

Explanation:

$"express the bases on both sides in terms of " color(blue)"base 2"$

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

$rArr2^(6x)=2^((3x-6))$

$"since the bases are equal we can equate the exponents"$

$rArr6x=3x-6$

$rArr3x=-6$

$rArrx=-2$

$color(blue)"As a check"$

$"left side "=4^(-6)=1/(4^6)=1/4096$

$"right side "=8^(-4)=1/8^4=1/4096$

$rArrx=-2" is the solution"$

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Solve $4^(3x)=8^(x-2)$ ? Thank You.

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