Chapter EP, Problem 8.3.7EP

To determine

The value of logarithmic expression.

Explanation of Solution

Given information:

The given equation is ${\log }_{4}16$

Calculations:

To convert the logarithmic function into exponential function, we should know the concept below.

Let $b$ and $x$ be positive numbers with $b\ne 0$ . The logarithm of x with base b is denoted is denoted by ${\log }_{b}x$ and is defined as exponent $y$ that makes the equation $b^y=x$ true.

Following the rule we can convert the equation in exponential form. Then we can find the value of the expression.

  $\begin{array}{l}{\log }_{4}16=y\\ 4^y=16\\ 4^y=4^4\\ \text{comparing both sides we can write,}\\ y=4\\ Thus,\\ {\log }_{4}16=4\end{array}$