Question

solve $3^x = 7$. round your answer to the nearest thousandth.
$x\approx\square$

Explanation:

Step1: Apply natural log to both sides

$\ln(3^x) = \ln(7)$

Step2: Use log power rule to simplify left side

$x\ln(3) = \ln(7)$

Step3: Isolate x by dividing both sides by $\ln(3)$

$x = \frac{\ln(7)}{\ln(3)}$

Step4: Calculate and round to thousandth

$x \approx \frac{1.945910149}{1.098612289} \approx 1.771$

Answer:

$x \approx 1.771$