Solve 4^p=16*2^34

$$4 ^ { p } = 16 \times 2 ^ { 34 }$$

Solve for p

$$p=19$$

Steps Using Definition of Logarithm

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

$$4^{p}=274877906944$$

Take the logarithm of both sides of the equation.

$$\log(4^{p})=\log(274877906944)$$

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

$$p\log(4)=\log(274877906944)$$

Divide both sides by \log(4).

$$p=\frac{\log(274877906944)}{\log(4)}$$

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

$$p=\log_{4}\left(274877906944\right)$$