Q 102. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation. 

$e^{-2x+1}=13$

Step-by-Step Solution

Answer

The solution to the equation, $e^{-2x+1}=13$is, $x=\frac{1}{2}(1-\ln 13)$.

Step 1. Given Information

The given equation to be solved is $e^{-2x+1}=13$.

Step 2. Formula used

Natural logarithm: 

$\ln e=1$

Step 3. Finding Solution

The given equation is $e^{-2x+1}=13$.

Take logarithm on both sides.
$$\begin{gathered} \ln e^{-2x+1}=\ln 13 \\ (-2x+1)\ln e=\ln 13 \\ -2x+1=\ln 13 \\ -2x=\ln 13-1 \\ x=\frac{1}{2}(1-\ln 13) \end{gathered}$$

The solution to the given equation is,  $x=\frac{1}{2}(1-\ln 13)$.