Chapter 13.3, Problem 72STP

To determine

To find: Solve each equation.

Answer to Problem 72STP

  $x\approx 1.3802$

Explanation of Solution

Given information:

  $3^{x+2}=41$

Given

  $3^{x+2}=41$

Using the logarithm functions

We get

  $\begin{array}{l}{3}^{x+2}=41\\ \Rightarrow \log \left(3^{x+2}\right)=\log \left(41\right)\\ \Rightarrow \left(x+2\right)\log \left(3\right)=\log \left(41\right)\\ \Rightarrow \left(x+2\right)\frac{\log \left(3\right)}{\log \left(3\right)}=\frac{\log \left(41\right)}{\log \left(3\right)}\\ \Rightarrow \left(x+2\right)=\frac{\log \left(41\right)}{\log \left(3\right)}\\ \Rightarrow \left(x+2\right)-2=\frac{\log \left(41\right)}{\log \left(3\right)}-2\\ \Rightarrow x=\frac{\log \left(41\right)}{\log \left(3\right)}-2\\ \Rightarrow x=\frac{1.6128}{0.4771}-2\\ \Rightarrow x=3.3802-2\\ \Rightarrow x=1.3802\end{array}$

Therefore,

  $x\approx 1.3802$