Question

What is the solution to the equation below? Round your answer to two decimal places.3x = 9.2A.x = 2.02B.x = 2.22C.x = 0.50D.x = 0.96

Answer 1

A)2.02

Explanation

Step 1

given

$3^x=9.2$

a) write the rigth side of the equation as a fraction

$9.2=\frac{92}{10}=\frac{46}{5}$

hence

$3^x=\frac{46}{5}$

b) take the logarithms in both sides

$\begin{gathered} 3^x=\frac{46}{5} \\ \ln3^x=ln\frac{46}{5} \\ apply\text{ the property} \\ x=log_3(\frac{46}{5}) \\ x=2.02 \end{gathered}$

so, the answer is

A)2.02