Solve 10000*(1.2)^x=10000000

$$10000 \times ( 1.2 ) ^ { x } = 10000000$$

Solve for x

$$x=3\log_{1.2}\left(10\right)\approx 37.88775941$$

Steps Using Definition of Logarithm

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

$$10000\times 1.2^{x}=10000000$$

Divide both sides by 10000.

$$1.2^{x}=1000$$

Take the logarithm of both sides of the equation.

$$\log(1.2^{x})=\log(1000)$$

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

$$x\log(1.2)=\log(1000)$$

Divide both sides by \log(1.2).

$$x=\frac{\log(1000)}{\log(1.2)}$$

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

$$x=\log_{1.2}\left(1000\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.2)}+3\log_{1.2}\left(10\right)$$

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