Question

Solve the logarithmic equation. When necessary, round answer to the nearest hundredth.

4-3 In x=-8
a. x =1.39
b. x = 4
c. x = 54.6

Answer 1

To solve the equation 4 - 3 ln(x) = -8, we need to isolate ln(x), exponentiate both sides with base 'e' to solve for x, and then use a calculator to find its value. The correct solution when rounded to the nearest hundredth is x = 54.6. The correct answer is option c.

Step-by-step explanation:

The equation we are trying to solve is 4 - 3 ln(x) = -8. To isolate the variable, we'll first move the constant term on the left to the other side of the equation:

3 ln(x) = 4 + 8

3 ln(x) = 12

Now, we divide both sides by 3 to solve for ln(x):

ln(x) = 12 / 3

ln(x) = 4

Next, we exponentiate both sides with base 'e' to eliminate the natural logarithm:

e^ln(x) = e^4

x = e^4

Using a calculator to find the value of e^4 and rounding to the nearest hundredth:

x ≈ 54.60

Therefore, the correct option that solves the equation is c. x = 54.6.