Question

question
solve for x:
$81^{x - 2} = 27^{2x}$
answer
attempt 1 out of 2
$x = \square$ submit answer

Explanation:

Step1: Rewrite bases as powers of 3

$81 = 3^4$, $27 = 3^3$, so substitute:
$$3^{4(x-2)} = 3^{3(2x)}$$

Step2: Simplify exponents

Distribute coefficients in exponents:
$$3^{4x-8} = 3^{6x}$$

Step3: Set exponents equal

Since bases are equal, exponents are equal:
$4x - 8 = 6x$

Step4: Solve for x

Rearrange terms to isolate x:
$-8 = 6x - 4x$
$2x = -8$
$x = \frac{-8}{2}$

Answer:

$x = -4$