Solve 1444.89/800=1.03^x

$$\frac{ 1444.89 }{ 800 } = { 1.03 }^{ x }$$

Solve for x

$$x=\log_{1.03}\left(1.8061125\right)\approx 20.000023701$$

Steps Using Definition of Logarithm

Expand \frac{1444.89}{800} by multiplying both numerator and the denominator by 100.

$$\frac{144489}{80000}=1.03^{x}$$

Swap sides so that all variable terms are on the left hand side.

$$1.03^{x}=\frac{144489}{80000}$$

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

$$1.03^{x}=1.8061125$$

Take the logarithm of both sides of the equation.

$$\log(1.03^{x})=\log(1.8061125)$$

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

$$x\log(1.03)=\log(1.8061125)$$

Divide both sides by \log(1.03).

$$x=\frac{\log(1.8061125)}{\log(1.03)}$$

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

$$x=\log_{1.03}\left(1.8061125\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.03)}+\log_{1.03}\left(1.8061125\right)$$

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