Question

solve. round your answer to the nearest thousandth.
8 = 3^x
x =
submit

Explanation:

Step1: Take log of both sides

To solve for \( x \) in the equation \( 8 = 3^x \), we can take the logarithm of both sides. Using the natural logarithm (ln) for this purpose, we get:
\( \ln(8) = \ln(3^x) \)

Step2: Apply logarithm power rule

By the power rule of logarithms, \( \ln(a^b) = b\ln(a) \), so we can rewrite the right - hand side as:
\( \ln(8)=x\ln(3) \)

Step3: Solve for x

To isolate \( x \), we divide both sides of the equation by \( \ln(3) \):
\( x = \frac{\ln(8)}{\ln(3)} \)

We know that \( \ln(8)\approx2.0794415417 \) and \( \ln(3)\approx1.0986122887 \). Then:
\( x=\frac{2.0794415417}{1.0986122887}\approx1.893 \)

Answer:

\( 1.893 \)