Chapter 11.6, Problem 52E

To determine

The value of given equation by graphing.

Explanation of Solution

Given:

  ${10}^{x-3}=52$

Solution:

From the given equation,

  $\begin{array}{l}{10}^{x-3}=52\\ \ln {10}^{x-3}=\ln 52\left(\text{taking}\text{natural}\text{log}\right)\\ \left(x-3\right)\left(\ln 10\right)=\ln 52\left(\ln a^x=x\ln a\right)\\ \left(x-3\right)=\frac{\ln 52}{\left(\ln 10\right)}\\ \left(x-3\right)=1.7160\\ x=4.7160\end{array}$

The plot of the given equation:

  

Therefore,

The graph of the given equation is obtained.