Question

Solve: 3 ln x = ln 216

Answer 1

$3\ln x=\ln 216\\ \ln x^3 =\ln 216\\ x^3=216\\ x=6$

Answer 2

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).

Hope this helps!