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

Step-by-step explanation

Step 1

given

`3^x=9.2`

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

`9.2=(92)/(10)=(46)/(5)`

hence

`3^x=(46)/(5)`

b) take the logarithms in both sides

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

so, the answer is

A)2.02