Solve 6200=990(1.115)^x+2900

$$6200 = 990 ( 1.115 ) ^ { x } + 2900$$

Solve for x

$$x=\log_{1.115}\left(\frac{10}{3}\right)\approx 11.060395813$$

Steps Using Definition of Logarithm

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

$$990\times 1.115^{x}+2900=6200$$

Subtract 2900 from both sides of the equation.

$$990\times 1.115^{x}=3300$$

Divide both sides by 990.

$$1.115^{x}=\frac{10}{3}$$

Take the logarithm of both sides of the equation.

$$\log(1.115^{x})=\log(\frac{10}{3})$$

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

$$x\log(1.115)=\log(\frac{10}{3})$$

Divide both sides by \log(1.115).

$$x=\frac{\log(\frac{10}{3})}{\log(1.115)}$$

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

$$x=\log_{1.115}\left(\frac{10}{3}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.115)}+\log_{1.115}\left(\frac{10}{3}\right)$$

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