Question

question 8 of 10
what is the solution to the equation below? round your answer to two decimal places.
4e^(2x) + 16 = 36
a. x = 1.39
b. x = 1.61
c. x = 0.80
d. x = 3.22

Explanation:

Step1: Isolate the exponential term

Subtract 16 from both sides of the equation \(4e^{2x}+16 = 36\).
\(4e^{2x}=36 - 16\)
\(4e^{2x}=20\)

Step2: Solve for \(e^{2x}\)

Divide both sides by 4.
\(e^{2x}=\frac{20}{4}=5\)

Step3: Take the natural logarithm

Take the natural log of both sides: \(\ln(e^{2x})=\ln(5)\)
Using the property \(\ln(e^{a}) = a\), we get \(2x=\ln(5)\)

Step4: Solve for \(x\)

Divide both sides by 2: \(x=\frac{\ln(5)}{2}\)
Calculate \(\ln(5)\approx1.6094\), then \(x=\frac{1.6094}{2}\approx0.80\)

Answer:

C. \(x = 0.80\)