Chapter 3, Problem 114RE

To determine

To solve the logarithmic equation

  ${\log }_{10}\left(-x-4\right)=2$

Answer to Problem 114RE

  $x=-104$

Explanation of Solution

Given:

  ${\log }_{10}\left(-x-4\right)=2$

Concept Used:

For $a\in R^{+}\&a\ne 1$ and $u\in R^{+}$ :

  ${\log }_{a}u=x\iff u=a^x$

  $a^{{\log }_{a}x}=x$

Calculation:

In order to solve the logarithmic equation

  ${\log }_{10}\left(-x-4\right)=2$

First convert it into exponential equation using the property ${\log }_{a}u=x\iff u=a^x$ .

As,

  $\begin{array}{c}{\log }_{10}\left(-x-4\right)=2\\ \left(-x-4\right)={10}^2\\ -x-4=100\end{array}$

Now simplify it further to find value of x.

As,

  $\begin{array}{c}-x-4=100\\ x=-100-4\\ x=-104\end{array}$

Thus, solution of given equation is $x=-104$ .