Question

question 3 of 10
what is the solution to the equation below? round your answer to two decimal places.
5 + 8·ln x = 15.8

a. x = 3.67
b. x = 2.26
c. x = 0.30
d. x = 3.86

Explanation:

Step1: Isolate the logarithmic term

Subtract 5 from both sides of the equation \(5 + 8\cdot\ln x = 15.8\).
\(8\cdot\ln x = 15.8 - 5\)
\(8\cdot\ln x = 10.8\)

Step2: Solve for \(\ln x\)

Divide both sides by 8.
\(\ln x=\frac{10.8}{8}\)
\(\ln x = 1.35\)

Step3: Exponentiate to solve for \(x\)

Since \(\ln x = 1.35\) and \(\ln x=\log_{e}x\), we exponentiate both sides with base \(e\):
\(x = e^{1.35}\)
Using a calculator, \(e^{1.35}\approx3.86\) (rounded to two decimal places).

Answer:

D. \(x = 3.86\)