Q 107. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation.

Step-by-Step Solution

Answer

The solution to the equation, 

$5e^{0.2x}=7$

Step 1. Given Information

The given equation to be solved is $5e^{0.2x}=7$is, $x=5\ln \frac{7}{5}$.

Step 2. Formula used

Natural logarithm: 

$\ln e=1$

Step 3. Finding Solution

The given equation is $5e^{0.2x}=7$.

Divide both sides by $5$.

$\frac{5e^{0.2x}}{5}=\frac{7}{5}$

$e^{0.2x}=\frac{7}{5}$

Take logarithm on both sides.

$\ln e^{0.2x}=\ln \frac{7}{5}$

$0.2x\ln e=\ln \frac{7}{5}$

$0.2x=\ln \frac{7}{5}$

$x=5\ln \frac{7}{5}$

The solution to the given equation is,  $x=5\ln \frac{7}{5}$.