Question

find the solution of the exponential equation
$2e^{x}-20 = 18$
in terms of logarithms, or correct to four decimal places.
$x=$
question help: video 1 video 2

Explanation:

Step1: Isolate the exponential term

$$\begin{align*} 2e^{x}-20&=18\\ 2e^{x}&=18 + 20\\ 2e^{x}&=38\\ e^{x}&=\frac{38}{2}\\ e^{x}& = 19 \end{align*}$$

Step2: Solve for \(x\) using the natural logarithm

Since \(y = e^{x}\) is equivalent to \(x=\ln(y)\) (where \(\ln\) is the natural logarithm, base \(e\)), when \(e^{x}=19\), we have \(x=\ln(19)\).
Using a calculator, \(\ln(19)\approx2.9444\)

Answer:

\(x=\ln(19)\approx2.9444\)