Solve 4599*1.25^x=10000

$$4599 \times { 1.25 }^{ x } =10000$$

Solve for x

$$x=\log_{1.25}\left(\frac{10000}{4599}\right)\approx 3.480926067$$

Steps Using Definition of Logarithm

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

$$4599\times 1.25^{x}=10000$$

Divide both sides by 4599.

$$1.25^{x}=\frac{10000}{4599}$$

Take the logarithm of both sides of the equation.

$$\log(1.25^{x})=\log(\frac{10000}{4599})$$

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

$$x\log(1.25)=\log(\frac{10000}{4599})$$

Divide both sides by \log(1.25).

$$x=\frac{\log(\frac{10000}{4599})}{\log(1.25)}$$

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

$$x=\log_{1.25}\left(\frac{10000}{4599}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.25)}+\log_{1.25}\left(\frac{10000}{4599}\right)$$

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