Solve (7/3)^-2*(3/7)^14=(7/3)^8m

$$( \frac { 7 } { 3 } ) ^ { - 2 } \times ( \frac { 3 } { 7 } ) ^ { 14 } = ( \frac { 7 } { 3 } ) ^ { 8 m }$$

Solve for m

$$m=-2$$

Steps Using Definition of Logarithm

Calculate \frac{7}{3} to the power of -2 and get \frac{9}{49}.

$$\frac{9}{49}\times \left(\frac{3}{7}\right)^{14}=\left(\frac{7}{3}\right)^{8m}$$

Calculate \frac{3}{7} to the power of 14 and get \frac{4782969}{678223072849}.

$$\frac{9}{49}\times \frac{4782969}{678223072849}=\left(\frac{7}{3}\right)^{8m}$$

Multiply \frac{9}{49} and \frac{4782969}{678223072849} to get \frac{43046721}{33232930569601}.

$$\frac{43046721}{33232930569601}=\left(\frac{7}{3}\right)^{8m}$$

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

$$\left(\frac{7}{3}\right)^{8m}=\frac{43046721}{33232930569601}$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{7}{3}\right)^{8m})=\log(\frac{43046721}{33232930569601})$$

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

$$8m\log(\frac{7}{3})=\log(\frac{43046721}{33232930569601})$$

Divide both sides by \log(\frac{7}{3}).

$$8m=\frac{\log(\frac{43046721}{33232930569601})}{\log(\frac{7}{3})}$$

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

$$8m=\log_{\frac{7}{3}}\left(\frac{43046721}{33232930569601}\right)$$

Divide both sides by 8.

$$m=-\frac{16}{8}$$