Solve 5579000*1.035^x=27000000000

$$5579000 \times { 1.035 }^{ x } =27000000000$$

Solve for x

$$x=\log_{1.035}\left(\frac{27000000}{5579}\right)\approx 246.634613902$$

Steps Using Definition of Logarithm

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

$$5579000\times 1.035^{x}=27000000000$$

Divide both sides by 5579000.

$$1.035^{x}=\frac{27000000}{5579}$$

Take the logarithm of both sides of the equation.

$$\log(1.035^{x})=\log(\frac{27000000}{5579})$$

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

$$x\log(1.035)=\log(\frac{27000000}{5579})$$

Divide both sides by \log(1.035).

$$x=\frac{\log(\frac{27000000}{5579})}{\log(1.035)}$$

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

$$x=\log_{1.035}\left(\frac{27000000}{5579}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.035)}+\log_{1.035}\left(\frac{27000000}{5579}\right)$$

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