Solve 27^m=19683

$$27 ^ { m } = 19683$$

Solve for m

$$m=3$$

Steps Using Definition of Logarithm

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

$$27^{m}=19683$$

Take the logarithm of both sides of the equation.

$$\log(27^{m})=\log(19683)$$

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

$$m\log(27)=\log(19683)$$

Divide both sides by \log(27).

$$m=\frac{\log(19683)}{\log(27)}$$

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

$$m=\log_{27}\left(19683\right)$$

Solve for m (complex solution)

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

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