Solve 5000=1,042^x

$$5000 = 1,042 ^ { x }$$

Solve for x

$$x=\log_{1042}\left(5000\right)\approx 1.225689907$$

Steps Using Definition of Logarithm

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

$$1042^{x}=5000$$

Take the logarithm of both sides of the equation.

$$\log(1042^{x})=\log(5000)$$

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

$$x\log(1042)=\log(5000)$$

Divide both sides by \log(1042).

$$x=\frac{\log(5000)}{\log(1042)}$$

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

$$x=\log_{1042}\left(5000\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1042)}+\log_{1042}\left(5000\right)$$

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