Solve 8^6y+4=64

$$8 ^ { 6 y + 4 } = 64$$

Solve for y

$$y=-\frac{1}{3}\approx -0.333333333$$

Steps Using Definition of Logarithm

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

$$8^{6y+4}=64$$

Take the logarithm of both sides of the equation.

$$\log(8^{6y+4})=\log(64)$$

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

$$\left(6y+4\right)\log(8)=\log(64)$$

Divide both sides by \log(8).

$$6y+4=\frac{\log(64)}{\log(8)}$$

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

$$6y+4=\log_{8}\left(64\right)$$

Subtract 4 from both sides of the equation.

$$6y=2-4$$

Divide both sides by 6.

$$y=-\frac{2}{6}$$