Solve the equation. Give the exact solution
-$9^{x}=81(3 x-3)$

A) $\frac{3}{10}$

B) $\frac{6}{5}$

C) $\frac{3}{2}$

D) $-\frac{6}{5}$

Name: Solve the equation. Give the exact solution -$9^{x}=81(3 x-3)$ A) $\frac{3}{10}$ B) $\frac{6}{5}$ C) $\frac{3}{2}$ D) $-\frac{6}{5}$
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Question

Solve the equation. Give the exact solution
-$9^{x}=81(3 x-3)$

A) $\frac{3}{10}$

B) $\frac{6}{5}$

C) $\frac{3}{2}$

D) $-\frac{6}{5}$

Quizplus · Accepted Answer

First, express 81 as $9^{\frac{3}{2}}$. Then, rewrite the equation as $9^x = 9^{\frac{3}{2}}(3x - 3)$. Equating the exponents gives $x = \frac{3}{2} + \log_9(3x - 3)$. Solving this equation gives $x = \frac{6}{5}$.

Solve the Equation 9x=81(3x−3)9^{x}=81(3 x-3)9x=81(3x−3) A) 310\frac{3}{10}103​ B) 65\frac{6}{5}56​ C) 32\frac{3}{2}23​ D) −65-\frac{6}{5}−56​

Solve the Equation $9^{x}=81(3 x-3)$ A) $\frac{3}{10}$ B) $\frac{6}{5}$ C) $\frac{3}{2}$ D) $-\frac{6}{5}$