Chapter 4.4, Problem 8QR

To determine

To calculate:The solution of the given expression.

Answer to Problem 8QR

The exact answer is $\frac{\ln 19}{\ln 13}$ .

Explanation of Solution

Given information:The expression is given as,

  $3^x=19$

Formula used:

  $\log \left(x^a\right)=a\log x$ ......... (1)

Calculation:Using the equation given in equation (1),

  $\begin{array}{l}{3}^x=19\\ \text{Take}\text{logarithm}\text{both}\text{sides,}\\ \ln 3^x=\ln 19\\ x\ln 3=\ln 19\\ x=\frac{\ln 19}{\ln 13}\end{array}$

The given value is converted as $\frac{\ln 19}{\ln 13}$ .