Question

question
solve for ( x ), rounding to the nearest hundredth.
( 3^x = 37 )

Explanation:

Step1: Apply logarithm to both sides

Take $\log$ of both sides: $\log(3^x) = \log(37)$

Step2: Use logarithm power rule

Bring down exponent: $x\log(3) = \log(37)$

Step3: Isolate $x$

Rearrange to solve for $x$: $x = \frac{\log(37)}{\log(3)}$

Step4: Calculate and round

Compute value, round to hundredth: $x \approx \frac{1.5682}{0.4771} \approx 3.29$

Answer:

$x \approx 3.29$