Question

What is the solution to the equation below? Round your answer to two decimal places.3x = 21A.x = 2.77B.x = 1.32C.x = 0.36D.x = 3.04

Answer 1

Given: The equation below

$3^x=21$

To Determine: The value of x

Solution

Let us apply the exponent rule

$\begin{gathered} 3^x=21 \\ xln3=ln21 \end{gathered}$$\begin{gathered} xln3=ln21 \\ x=\frac{ln21}{ln3} \end{gathered}$$\begin{gathered} x=\frac{3.0445}{1.0986} \\ x=2.7712 \\ x\approx2.77 \end{gathered}$

Hence, the approximate value of x is 2.77, OPTION A