Q 108. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation.

$8·{10}^{2x-7}=3$

Step-by-Step Solution

Answer

The solution to the equation, $8·{10}^{2x-7}=3$is, $x=\frac{1}{2}\left(\log \frac{3}{8}+7\right)$.

Step 1. Given Information

The given equation to be solved is  $8·{10}^{2x-7}=3$.

Step 2. Formula used

Common logarithm: 

$\log 10=1$

Step 3. Finding Solution

The given equation is $8·{10}^{2x-7}=3$

Divide both sides by $8$.

$$\begin{gathered} \frac{8·{10}^{2x-7}}{8}=\frac{3}{8} \\ {10}^{2x-7}=\frac{3}{8} \end{gathered}$$

Take logarithm on both sides.
$$\begin{gathered} \log {10}^{2x-7}=\log \frac{3}{8} \\ (2x-7)\log 10=\log \frac{3}{8} \\ 2x-7=\log \frac{3}{8} \\ 2x=\log \frac{3}{8}+7 \\ x=\frac{1}{2}\left(\log \frac{3}{8}+7\right) \end{gathered}$$

The solution to the given equation is, $x=\frac{1}{2}\left(\log \frac{3}{8}+7\right)$.