Solve 1500000000=1096787072*1.11^x

$$1500000000=1096787072 \times { 1.11 }^{ x }$$

Solve for x

$$x=\log_{1.11}\left(\frac{11718750}{8568649}\right)\approx 3$$

Steps Using Definition of Logarithm

Divide both sides by 1096787072.

$$\frac{1500000000}{1096787072}=1.11^{x}$$

Reduce the fraction \frac{1500000000}{1096787072} to lowest terms by extracting and canceling out 128.

$$\frac{11718750}{8568649}=1.11^{x}$$

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

$$1.11^{x}=\frac{11718750}{8568649}$$

Take the logarithm of both sides of the equation.

$$\log(1.11^{x})=\log(\frac{11718750}{8568649})$$

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

$$x\log(1.11)=\log(\frac{11718750}{8568649})$$

Divide both sides by \log(1.11).

$$x=\frac{\log(\frac{11718750}{8568649})}{\log(1.11)}$$

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

$$x=\log_{1.11}\left(\frac{11718750}{8568649}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.11)}+\log_{1.11}\left(\frac{11718750}{8568649}\right)$$

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