Solve -3*4^-10n=-39

$$- 3 \cdot 4 ^ { - 10 n } = - 39$$

Solve for n

$$n=-\frac{\log_{2}\left(13\right)}{20}\approx -0.185021986$$

Steps Using Definition of Logarithm

Divide both sides by -3.

$$4^{-10n}=\frac{-39}{-3}$$

Divide -39 by -3 to get 13.

$$4^{-10n}=13$$

Take the logarithm of both sides of the equation.

$$\log(4^{-10n})=\log(13)$$

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

$$-10n\log(4)=\log(13)$$

Divide both sides by \log(4).

$$-10n=\frac{\log(13)}{\log(4)}$$

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

$$-10n=\log_{4}\left(13\right)$$

Divide both sides by -10.

$$n=\frac{\log_{2}\left(13\right)}{-10\times 2}$$