Solve 1.08^y=1.36

$$1.08 ^ { y } = 1.36$$

Solve for y

$$y=\log_{1.08}\left(1.36\right)\approx 3.995329263$$

Steps Using Definition of Logarithm

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

$$1.08^{y}=1.36$$

Take the logarithm of both sides of the equation.

$$\log(1.08^{y})=\log(1.36)$$

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

$$y\log(1.08)=\log(1.36)$$

Divide both sides by \log(1.08).

$$y=\frac{\log(1.36)}{\log(1.08)}$$

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

$$y=\log_{1.08}\left(1.36\right)$$

Solve for y (complex solution)

$$y=\frac{i\times 2\pi n_{1}}{\ln(1.08)}+\log_{1.08}\left(1.36\right)$$

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