Note: Enter your answer and SHOW ALL THE STEPS NECESSARY to solve this problem in the space provided. You will not receive credit without all work shown.
Solve algebraically. Round to the nearest thousandth.
In(5x-1)=4
To solve the equation ln(5x-1) = 4 algebraically, we first need to isolate x.
1. Use the property of logarithms that ln(a) = b is equivalent to e^b = a.
Therefore, we can rewrite the equation ln(5x-1) = 4 as e^4 = 5x-1.
2. Solve for x by adding 1 to both sides and then dividing by 5.
e^4 + 1 = 5x
x = (e^4 + 1) / 5
3. Now, compute the value of x by plugging in e^4 ≈ 54.598 into the equation.
x ≈ (54.598 + 1) / 5
x ≈ 55.598 / 5
x ≈ 11.120
Therefore, the solution to the equation ln(5x-1) = 4 rounded to the nearest thousandth is x ≈ 11.120.