Question

question 1 of 10
what is the solution to the equation below? round your answer to two decimal places.
( e^x = 7.9 )

a. ( x approx 275.26 )
b. ( x approx 2.07 )
c. ( x approx 0.90 )
d. ( x approx 2697.28 )

Explanation:

Step1: Apply natural logarithm

To solve \( e^{x}=7.9 \), take the natural logarithm (ln) of both sides. Recall that \( \ln(e^{x}) = x \) because the natural logarithm and the exponential function (with base \( e \)) are inverse functions. So we have:
\( \ln(e^{x})=\ln(7.9) \)
Which simplifies to:
\( x = \ln(7.9) \)

Step2: Calculate the value

Using a calculator, we find the value of \( \ln(7.9) \). The natural logarithm of 7.9 is approximately 2.07 (when rounded to two decimal places).

Answer:

B. \( x \approx 2.07 \)