Question

solve. write your answer in simplest form using integers, fractions, and natural logarithms. 42 = e^x + 1 x =

Explanation:

Step1: Isolate the exponential term

Subtract 1 from both sides of the equation \(42 = e^{x}+1\) to get \(e^{x}=42 - 1\).
\(e^{x}=41\)

Step2: Take the natural logarithm of both sides

Since the exponential function \(y = e^{x}\) and the natural logarithm function \(y=\ln(x)\) are inverse functions, we take the natural logarithm of both sides of \(e^{x}=41\).
Applying \(\ln\) to both sides gives \(\ln(e^{x})=\ln(41)\).

Step3: Simplify the left - hand side

Using the property of logarithms \(\ln(e^{a})=a\) (where \(a = x\) in our case), the left - hand side simplifies to \(x\). So \(x=\ln(41)\)

Answer:

\(\ln(41)\)