Solve 8^p=50

$$8 ^ { p } = 50$$

Solve for p

$$p = \frac{\log_{2} {(50)}}{3} \approx 1.881285397$$

Steps Using Definition of Logarithm

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

$$8^{p}=50$$

Take the logarithm of both sides of the equation.

$$\log(8^{p})=\log(50)$$

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

$$p\log(8)=\log(50)$$

Divide both sides by \log(8).

$$p=\frac{\log(50)}{\log(8)}$$

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

$$p=\log_{8}\left(50\right)$$

Solve for p (complex solution)

$$p=\frac{2\pi n_{1}i}{3\ln(2)}+\frac{\log_{2}\left(50\right)}{3}$$

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