Solve 3^p=243

$$3 ^ { p } = 243$$

Solve for p

$$p=5$$

Steps Using Definition of Logarithm

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

$$3^{p}=243$$

Take the logarithm of both sides of the equation.

$$\log(3^{p})=\log(243)$$

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

$$p\log(3)=\log(243)$$

Divide both sides by \log(3).

$$p=\frac{\log(243)}{\log(3)}$$

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

$$p=\log_{3}\left(243\right)$$

Solve for p (complex solution)

$$p=\frac{2\pi n_{1}i}{\ln(3)}+5$$

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