Chapter 4.6, Problem 47E

Solution

To find: The exponential and the logarithmic equation whose solutions are $4$ and $-3$ respectively.

Exponential equation: $2^x=16$

Logarithmic equation: $\ln \left(x+4\right)=0$

Given:

Solution of exponential equation= $4$

Solution of the logarithmic equation: $-3$

Calculation:

The form of the exponential equation is $y=a{b}^x$.

It is understood that $x=4$ . Now assume $a=1$ and $b=2$ then,

  $\begin{array}{l}y=1{\left(2\right)}^4\\ y=16\end{array}$

So, the example of an exponential equation having a solution $4$ is,

  $2^x=16$

And the example of the logarithm equation having a solution $-3$ is,

  $\ln \left(x+4\right)=0$

Conclusion:

The example of the exponential and the logarithm equations are $2^x=16$ and $\ln \left(x+4\right)=0$ respectively.