Question

solve. write your answer in simplest form using integers, fractions, and natural logarithms. 89 = e^x - 2 x =

Explanation:

Step1: Isolate the exponential term

We start with the equation \( 89 = e^{x}-2 \). To isolate \( e^{x} \), we add 2 to both sides of the equation.
\( 89 + 2=e^{x}-2 + 2 \)
\( 91 = e^{x} \)

Step2: Take the natural logarithm of both sides

Since \( y = e^{x} \) and \( y=\ln(x) \) are inverse functions, we can take the natural logarithm of both sides to solve for \( x \). Taking \( \ln \) of both sides of \( 91 = e^{x} \), we get:
\( \ln(91)=\ln(e^{x}) \)
By the property of logarithms \( \ln(e^{a})=a \), so \( \ln(e^{x}) = x \). Thus, \( x=\ln(91) \)

Answer:

\( \ln(91) \)