Chapter 11.5, Problem 43E

To determine

To Find: The solution for the equation or the inequality.

Answer to Problem 43E

The required solution is $x=0.3434$ .

Explanation of Solution

Given:

The given equation is,

  ${0.16}^{4+3x}={0.3}^{8-x}$

Calculation:

Consider the given equation is,

  ${0.16}^{4+3x}={0.3}^{8-x}$

Solve the inequality as,

  $\begin{array}{l}\log {0.16}^{4+3x}=\log {0.3}^{8-x}\\ \left(4+3x\right)\log 0.16=\left(8-x\right)\log 0.3\\ 4+3x=\left(8-x\right)\frac{\log 0.3}{\log 0.16}\\ 4+3x=\left(8-x\right)0.657\end{array}$

Solve further as,

  $\begin{array}{l}3x+0.657x=5.256-4\\ 3.657x=1.256\\ x=0.3434\end{array}$