Solve 8=5*4^t

$$8 = 5 \cdot 4 ^ { t }$$

Solve for t

$$t=\frac{-\log_{2}\left(5\right)+3}{2}\approx 0.339035953$$

Steps Using Definition of Logarithm

Divide both sides by 5.

$$\frac{8}{5}=4^{t}$$

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

$$4^{t}=\frac{8}{5}$$

Take the logarithm of both sides of the equation.

$$\log(4^{t})=\log(\frac{8}{5})$$

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

$$t\log(4)=\log(\frac{8}{5})$$

Divide both sides by \log(4).

$$t=\frac{\log(\frac{8}{5})}{\log(4)}$$

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

$$t=\log_{4}\left(\frac{8}{5}\right)$$