Question

solve. round your answer to the nearest thousandth.\\(9^{3x + 2} = 7\\)\\(x = \\)

Explanation:

Step1: Take log of both sides

$\log(9^{3x+2}) = \log(7)$

Step2: Apply log power rule

$(3x+2)\log(9) = \log(7)$

Step3: Isolate the linear term

$3x+2 = \frac{\log(7)}{\log(9)}$

Step4: Calculate log ratio

$3x+2 \approx \frac{0.8451}{0.9542} \approx 0.8857$

Step5: Solve for 3x

$3x = 0.8857 - 2 = -1.1143$

Step6: Solve for x

$x = \frac{-1.1143}{3} \approx -0.371$

Answer:

$-0.371$