Solve 1052*1.02^x=1073.04

$$1052 \times { 1.02 }^{ x } =1073.04$$

Solve for x

$$x=1$$

Steps Using Definition of Logarithm

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

$$1052\times \left(\frac{51}{50}\right)^{x}=1073.04$$

Divide both sides by 1052.

$$\left(\frac{51}{50}\right)^{x}=1.02$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{51}{50}\right)^{x})=\log(1.02)$$

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

$$x\log(\frac{51}{50})=\log(1.02)$$

Divide both sides by \log(\frac{51}{50}).

$$x=\frac{\log(1.02)}{\log(\frac{51}{50})}$$

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

$$x=\log_{\frac{51}{50}}\left(1.02\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.02)}+1$$

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