Solve 1.03045^x=4

$$1.03045 ^ { x } = 4$$

Solve for x

$$x=2\log_{1.03045}\left(2\right)\approx 46.216590416$$

Steps Using Definition of Logarithm

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

$$1.03045^{x}=4$$

Take the logarithm of both sides of the equation.

$$\log(1.03045^{x})=\log(4)$$

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

$$x\log(1.03045)=\log(4)$$

Divide both sides by \log(1.03045).

$$x=\frac{\log(4)}{\log(1.03045)}$$

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

$$x=\log_{1.03045}\left(4\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.03045)}+2\log_{1.03045}\left(2\right)$$

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