Solve 4^6y=9

$$4 ^ { 6 y } = 9$$

Solve for y

$$y=\frac{\log_{2}\left(3\right)}{6}\approx 0.264160417$$

Steps Using Definition of Logarithm

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

$$4^{6y}=9$$

Take the logarithm of both sides of the equation.

$$\log(4^{6y})=\log(9)$$

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

$$6y\log(4)=\log(9)$$

Divide both sides by \log(4).

$$6y=\frac{\log(9)}{\log(4)}$$

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

$$6y=\log_{4}\left(9\right)$$

Divide both sides by 6.

$$y=\frac{\log_{2}\left(3\right)}{6}$$