Solve 3^h-1=14

$$3 ^ { h - 1 } = 14$$

Solve for h

$$h=\log_{3}\left(14\right)+1\approx 3.402173503$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$3^{h-1}=14$$

Take the logarithm of both sides of the equation.

$$\log(3^{h-1})=\log(14)$$

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

$$\left(h-1\right)\log(3)=\log(14)$$

Divide both sides by \log(3).

$$h-1=\frac{\log(14)}{\log(3)}$$

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

$$h-1=\log_{3}\left(14\right)$$

Add 1 to both sides of the equation.

$$h=\log_{3}\left(14\right)-\left(-1\right)$$