Q 109. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation.

$2·{10}^{2-x}=5$

Step-by-Step Solution

Answer

The solution to the equation, $2·{10}^{2-x}=5$is, $x=2-\log \frac{5}{2}$.

Step 1. Given Information

The given equation to be solved is $2·{10}^{2-x}=5$.

Step 2. Formula used

Common Logarithm:
$\log 10=1$

Step 3. Finding Solution

The given equation is $2·{10}^{2-x}=5$.

Divide both sides by $2$.

$\frac{2·{10}^{2-x}}{2}=\frac{5}{2}$

${10}^{2-x}=\frac{5}{2}$

Take logarithm on both sides. 

$$\begin{gathered} \log {10}^{2-x}=\log \frac{5}{2} \\ (2-x)\log 10=\log \frac{5}{2} \\ 2-x=\log \frac{5}{2} \\ x=2-\log \frac{5}{2} \end{gathered}$$

The solution to the given equation is,  $x=2-\log \frac{5}{2}$.