To solve this problem, first we must understand that the coefficient of a log can also be expressed as the exponent of the argument. If we know this property, we can rewrite the equation as follows:
ln x^3 = ln 216
Next, we must use the inverse operation of ln to get rid of the logs on both sides. Because ln is really just a log with base e, if we make both sides of the equations the exponents of a base e, this will cancel the lns, and leave us with a simple equation.
e^ln(x^3) = e^ln216
This leaves us with:
x^3 = 216
If we take the cube root of each side to cancel out the degree 3 exponent on the variable x, we get that the answer is: x = 6 (Note: -6 is not an acceptable answer because (-6)^3 is actually -216).
