Question

what is the solution to the equation below? round your answer to two decimal places.
3 $e^x = 11.76$
a. $x = 0.59$
b. $x = 50.40$
c. $x = 40.98$
d. $x = 1.37$

Explanation:

Step1: Isolate the exponential term

Divide both sides of the equation \(3e^{x}=11.76\) by 3.
\(e^{x}=\frac{11.76}{3}\)
\(e^{x}=3.92\)

Step2: Take natural logarithm on both sides

\(\ln(e^{x})=\ln(3.92)\)
Since \(\ln(e^{x}) = x\) (by the property of logarithms \(\ln(e^{a})=a\)), we have:
\(x=\ln(3.92)\)

Step3: Calculate the natural logarithm

Using a calculator, \(\ln(3.92)\approx1.37\) (rounded to two decimal places).

Answer:

D. \(x = 1.37\)