Solve 4845=1.23^x

$$4845 = { 1.23 }^{ x }$$

Solve for x

$$x=\log_{1.23}\left(4845\right)\approx 40.990926126$$

Steps Using Definition of Logarithm

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

$$1.23^{x}=4845$$

Take the logarithm of both sides of the equation.

$$\log(1.23^{x})=\log(4845)$$

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

$$x\log(1.23)=\log(4845)$$

Divide both sides by \log(1.23).

$$x=\frac{\log(4845)}{\log(1.23)}$$

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

$$x=\log_{1.23}\left(4845\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.23)}+\log_{1.23}\left(4845\right)$$

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