Solve 700*(1.02)^x=800

$$700 \times ( 1.02 ) ^ { x } = 800$$

Solve for x

$$x=\log_{1.02}\left(\frac{8}{7}\right)\approx 6.743114973$$

Steps Using Definition of Logarithm

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

$$700\times 1.02^{x}=800$$

Divide both sides by 700.

$$1.02^{x}=\frac{8}{7}$$

Take the logarithm of both sides of the equation.

$$\log(1.02^{x})=\log(\frac{8}{7})$$

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

$$x\log(1.02)=\log(\frac{8}{7})$$

Divide both sides by \log(1.02).

$$x=\frac{\log(\frac{8}{7})}{\log(1.02)}$$

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

$$x=\log_{1.02}\left(\frac{8}{7}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.02)}+\log_{1.02}\left(\frac{8}{7}\right)$$

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