Solve 2*2^7m=2^36

$$2 \times 2 ^ { 7 m } = 2 ^ { 36 }$$

Solve for m

$$m=5$$

Steps Using Definition of Logarithm

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

$$2\times 2^{7m}=68719476736$$

Divide both sides by 2.

$$2^{7m}=34359738368$$

Take the logarithm of both sides of the equation.

$$\log(2^{7m})=\log(34359738368)$$

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

$$7m\log(2)=\log(34359738368)$$

Divide both sides by \log(2).

$$7m=\frac{\log(34359738368)}{\log(2)}$$

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

$$7m=\log_{2}\left(34359738368\right)$$

Divide both sides by 7.

$$m=\frac{35}{7}$$