Answer:
To solve the equation ln(6x - 1) = 5, you can use the properties of logarithms. First, you want to isolate the natural logarithm term, and then you can find x. Here's the step-by-step solution:
1. Start with the equation: ln(6x - 1) = 5.
2. Remove the natural logarithm by exponentiating both sides with base 'e' (the inverse operation of taking the natural logarithm):
e^(ln(6x - 1)) = e^5.
3. On the left side, e and ln cancel out, leaving you with:
6x - 1 = e^5.
4. Now, add 1 to both sides to isolate the term with x:
6x = e^5 + 1.
5. Finally, divide both sides by 6 to solve for x:
x = (e^5 + 1) / 6.
Now, calculate this value:
x ≈ (e^5 + 1) / 6 ≈ (148.41316 + 1) / 6 ≈ 24.23553 / 6 ≈ 4.04 (rounded to two decimal places).
So, the solution to the equation ln(6x - 1) = 5 is approximately x = 4.04 when rounded to two decimal places.
Step-by-step explanation: if you need a personal homework helper dm me on ig, savant.carlos