Solve 2*16^2n=70

$$2 \cdot 16 ^ { 2 n } = 70$$

Solve for n

$$n=\frac{\log_{2}\left(35\right)}{8}\approx 0.641160377$$

Steps Using Definition of Logarithm

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

$$2\times 16^{2n}=70$$

Divide both sides by 2.

$$16^{2n}=35$$

Take the logarithm of both sides of the equation.

$$\log(16^{2n})=\log(35)$$

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

$$2n\log(16)=\log(35)$$

Divide both sides by \log(16).

$$2n=\frac{\log(35)}{\log(16)}$$

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

$$2n=\log_{16}\left(35\right)$$

Divide both sides by 2.

$$n=\frac{\log_{2}\left(35\right)}{2\times 4}$$

Solve for n (complex solution)

$$n=\frac{\pi n_{1}i}{4\ln(2)}+\frac{\log_{2}\left(35\right)}{8}$$

$$n_{1}\in \mathrm{Z}$$