Question

what is the solution to the equation below? round your answer to two decimal places.
$3^x = 9.2$
a. $x \approx 0.96$
b. $x = 2.02$
c. $x = 2.22$
d. $x = 0.50$

Explanation:

Step1: Take log of both sides

Take the natural logarithm (ln) of both sides of the equation \(3^x = 9.2\). We get \(\ln(3^x)=\ln(9.2)\).

Step2: Use logarithm power rule

Using the power rule of logarithms \(\ln(a^b)=b\ln(a)\), the left - hand side becomes \(x\ln(3)=\ln(9.2)\).

Step3: Solve for x

To solve for \(x\), we divide both sides by \(\ln(3)\): \(x = \frac{\ln(9.2)}{\ln(3)}\).
We know that \(\ln(9.2)\approx2.2192\) and \(\ln(3)\approx1.0986\). Then \(x=\frac{2.2192}{1.0986}\approx2.02\).

Answer:

B. \(x = 2.02\)