Solve 25000*13^x=50000000

$$25000 \times 13 ^ { x } = 50000000$$

Solve for x

$$x=\log_{13}\left(2000\right)\approx 2.963373307$$

Steps Using Definition of Logarithm

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

$$25000\times 13^{x}=50000000$$

Divide both sides by 25000.

$$13^{x}=2000$$

Take the logarithm of both sides of the equation.

$$\log(13^{x})=\log(2000)$$

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

$$x\log(13)=\log(2000)$$

Divide both sides by \log(13).

$$x=\frac{\log(2000)}{\log(13)}$$

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

$$x=\log_{13}\left(2000\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(13)}+\log_{13}\left(2000\right)$$

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