Solve 5^F=20

$$5 ^ { F } = 20$$

Solve for F

$$F=\log_{5}\left(20\right)\approx 1.861353116$$

Steps Using Definition of Logarithm

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

$$5^{F}=20$$

Take the logarithm of both sides of the equation.

$$\log(5^{F})=\log(20)$$

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

$$F\log(5)=\log(20)$$

Divide both sides by \log(5).

$$F=\frac{\log(20)}{\log(5)}$$

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

$$F=\log_{5}\left(20\right)$$

Solve for F (complex solution)

$$F=\frac{2\pi n_{1}i}{\ln(5)}+\log_{5}\left(20\right)$$

$$n_{1}\in \mathrm{Z}$$