solve: ln12x = 6

To solve the equation ln(12x) = 6, we can use properties of logarithms to eliminate the natural logarithm (ln) and isolate the variable x.

Step 1: Eliminate the ln function
The natural logarithm (ln) of a number is the inverse of the exponential function with base e. Therefore, we can rewrite the equation as an exponential equation.

ln(12x) = 6 can be rewritten as e^(ln(12x)) = e^6

Step 2: Simplify the equation
Since e^(ln(12x)) is equal to 12x (inverse operations), the equation simplifies to 12x = e^6.

Step 3: Solve for x
To find the value of x, we need to divide both sides of the equation by 12:

12x = e^6

Divide both sides by 12:
x = e^6 / 12

The final solution is x = e^6 / 12, where e is the base of the natural logarithm, approximately equal to 2.71828.