Solve algebraically. Round to the nearest thousandth

Question

In(5x-1)=4

Answer 1

To solve this equation algebraically, we first need to isolate x.

Given: ln(5x-1) = 4

Step 1: Rewrite the equation in exponential form using the property of logarithms
5x - 1 = e^4

Step 2: Add 1 to both sides
5x = e^4 + 1

Step 3: Divide by 5
x = (e^4 + 1) / 5

Step 4: Evaluate the expression
x ≈ (54.598 + 1) /5

x ≈ 55.598 / 5

x ≈ 11.120

Therefore, the solution to the equation ln(5x-1) = 4 is x ≈ 11.120.