Solve 5(5^4)=5^m(125)

$$5 ( 5 ^ { 4 } ) = 5 ^ { m } ( 125 )$$

Solve for m

$$m=2$$

Steps Using Definition of Logarithm

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$5^{5}=5^{m}\times 125$$

Calculate 5 to the power of 5 and get 3125.

$$3125=5^{m}\times 125$$

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

$$5^{m}\times 125=3125$$

Divide both sides by 125.

$$5^{m}=\frac{3125}{125}$$

Divide 3125 by 125 to get 25.

$$5^{m}=25$$

Take the logarithm of both sides of the equation.

$$\log(5^{m})=\log(25)$$

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

$$m\log(5)=\log(25)$$

Divide both sides by \log(5).

$$m=\frac{\log(25)}{\log(5)}$$

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

$$m=\log_{5}\left(25\right)$$