Solve 3^5*3^0/3^-4=3^m

$$\frac { 3 ^ { 5 } \times 3 ^ { 0 } } { 3 ^ { - 4 } } = 3 ^ { m }$$

Solve for m

$$m=9$$

Steps Using Definition of Logarithm

To multiply powers of the same base, add their exponents. Add 5 and 0 to get 5.

$$\frac{3^{5}}{3^{-4}}=3^{m}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -4 from 5 to get 9.

$$3^{9}=3^{m}$$

Calculate 3 to the power of 9 and get 19683.

$$19683=3^{m}$$

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

$$3^{m}=19683$$

Take the logarithm of both sides of the equation.

$$\log(3^{m})=\log(19683)$$

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

$$m\log(3)=\log(19683)$$

Divide both sides by \log(3).

$$m=\frac{\log(19683)}{\log(3)}$$

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

$$m=\log_{3}\left(19683\right)$$