Solve 5=1.777^x

$$5= { 1.777 }^{ x }$$

Solve for x

$$x=\log_{1.777}\left(5\right)\approx 2.799380051$$

Steps Using Definition of Logarithm

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

$$1.777^{x}=5$$

Take the logarithm of both sides of the equation.

$$\log(1.777^{x})=\log(5)$$

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

$$x\log(1.777)=\log(5)$$

Divide both sides by \log(1.777).

$$x=\frac{\log(5)}{\log(1.777)}$$

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

$$x=\log_{1.777}\left(5\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.777)}+\log_{1.777}\left(5\right)$$

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