Question

Solve ln(3x-6)=5. Round to the nearest thousandth.

Answer 1

To solve ln(3x-6)=5, exponentiate both sides to get 3x-6=e^5. Then solve for x, which after calculations and rounding, results in x ≈ 51.471.

Step-by-step explanation:

To solve the equation ln⁽³ˣ⁻⁶⁾=5, first recall that the natural logarithm function is the inverse of the exponential function ex. Therefore, you can exponentiate both sides of the equation to cancel out the natural logarithm.

1. Express the equation as eln⁽³ˣ⁻⁶⁾= e5.
2. This simplifies to 3x - 6 = e5 because the natural logarithm and the exponential function are inverses.
3. Now, you can calculate e5 which approximately equals 148.413159. Adding 6 to both sides gives 3x = 148.413159 + 6 = 154.413159.
4. Finally, divide by 3 to solve for x: x = 154.413159 / 3 ≈ 51.471053.

Therefore, the solution to the equation rounded to the nearest thousandth is x ≈ 51.471.