Solve (4/3)^n=1000

$$( \frac { 4 } { 3 } ) ^ { n } = 1000$$

Solve for n

$$n=3\log_{\frac{4}{3}}\left(10\right)\approx 24.011768339$$

Steps Using Definition of Logarithm

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

$$\left(\frac{4}{3}\right)^{n}=1000$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{4}{3}\right)^{n})=\log(1000)$$

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

$$n\log(\frac{4}{3})=\log(1000)$$

Divide both sides by \log(\frac{4}{3}).

$$n=\frac{\log(1000)}{\log(\frac{4}{3})}$$

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

$$n=\log_{\frac{4}{3}}\left(1000\right)$$