Solve 5*27^x=10,935

$$5 \times 27 ^ { x } = 10,935$$

Solve for x

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Steps Using Definition of Logarithm

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

$$5\times 27^{x}=10935$$

Divide both sides by 5.

$$27^{x}=2187$$

Take the logarithm of both sides of the equation.

$$\log(27^{x})=\log(2187)$$

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

$$x\log(27)=\log(2187)$$

Divide both sides by \log(27).

$$x=\frac{\log(2187)}{\log(27)}$$

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

$$x=\log_{27}\left(2187\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(3)}+\frac{7}{3}$$

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