Solve (4+5)^5m+3=(5+4)^7

$$( 4 + 5 ) ^ { 5 m + 3 } = ( 5 + 4 ) ^ { 7 }$$

Solve for m

$$m=\frac{4}{5}=0.8$$

Steps Using Definition of Logarithm

Add 4 and 5 to get 9.

$$9^{5m+3}=\left(5+4\right)^{7}$$

Add 5 and 4 to get 9.

$$9^{5m+3}=9^{7}$$

Calculate 9 to the power of 7 and get 4782969.

$$9^{5m+3}=4782969$$

Take the logarithm of both sides of the equation.

$$\log(9^{5m+3})=\log(4782969)$$

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

$$\left(5m+3\right)\log(9)=\log(4782969)$$

Divide both sides by \log(9).

$$5m+3=\frac{\log(4782969)}{\log(9)}$$

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

$$5m+3=\log_{9}\left(4782969\right)$$

Subtract 3 from both sides of the equation.

$$5m=7-3$$

Divide both sides by 5.

$$m=\frac{4}{5}$$