Chapter 8.5, Problem 1CYU

To determine

To find: The value of logarithmic expression ${\log }_{4}18$ .

Answer to Problem 1CYU

The value of expression ${\log }_{4}18$ is $2.08500$ .

Explanation of Solution

Given:

The logarithmic expression is ${\log }_{4}18$ .

Calculation:

Rewrite the logarithmic expression ${\log }_{4}18$ as ${\log }_{4}18={\log }_4\left(2\times 9\right)$ .

Use the Multiplication Property of the logarithms to solve the equation ${\log }_{4}18={\log }_4\left(2\times 9\right)$ .

  $\begin{array}{c}{\log }_{4}18={\log }_4\left(2\times 9\right)\\ ={\log }_{4}2+{\log }_{4}9\\ ={\log }_4{4}^{1/2}+{\log }_4{3}^2\end{array}$

Use the Power Rule of logarithms to solve the above equation.

  $\begin{array}{c}{\log }_{4}18={\log }_4{4}^{1/2}+{\log }_4{3}^2\\ =\frac{1}{2}{\log }_{4}4+2{\log }_{4}3\\ \approx 2.08500\end{array}$

Therefore, the value of expression ${\log }_{4}18$ is $2.08500$ .