Solve 239=3^n-1

$$239 = 3 ^ { n - 1 }$$

Solve for n

$$n=\log_{3}\left(239\right)+1\approx 5.984891948$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

$$3^{n-1}=239$$

Take the logarithm of both sides of the equation.

$$\log(3^{n-1})=\log(239)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$\left(n-1\right)\log(3)=\log(239)$$

Divide both sides by \log(3).

$$n-1=\frac{\log(239)}{\log(3)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$n-1=\log_{3}\left(239\right)$$

Add 1 to both sides of the equation.

$$n=\log_{3}\left(239\right)-\left(-1\right)$$