Chapter 13.5, Problem 6MRE

To determine

If the value of the expression.

Explanation of Solution

Given information:

The given expression is

  ${\log }_b(-a)$

  $\begin{array}{l}a=-2\\ b=4\end{array}$

Calculations:

Here the given expression is ${\log }_b(-a)$ .

Now putting the value of a and b in the expression we get the value of the expression,

  $\begin{array}{l}{\log }_b(-a)\\ {\log }_4(-(-2))\\ {\log }_4(2)\end{array}$

To find the value of the logarithmic expression we have to convert the logarithmic function into exponential function, for this 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.

  $\begin{array}{l}{\log }_4(2)=y\\ 4^y=2\\ 4^y=4^{\frac{1}{2}}\\ \text{comparing both sides we can write,}\\ y=\frac{1}{2}\\ Thus,\\ {\log }_4(2)=\frac{1}{2}\end{array}$