Solve (1.04)^2n=2

$$( 1.04 ) ^ { 2 n } = 2$$

Solve for n

$$n = \frac{\log_{1.04} {(2)}}{2} \approx 8.836493843$$

Steps Using Definition of Logarithm

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

$$1.04^{2n}=2$$

Take the logarithm of both sides of the equation.

$$\log(1.04^{2n})=\log(2)$$

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

$$2n\log(1.04)=\log(2)$$

Divide both sides by \log(1.04).

$$2n=\frac{\log(2)}{\log(1.04)}$$

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

$$2n=\log_{1.04}\left(2\right)$$

Divide both sides by 2.

$$n=\frac{\ln(2)}{2\ln(\frac{26}{25})}$$