Solve 4^3w-5=3

$$4 ^ { 3 w } - 5 = 3$$

Solve for w

$$w=\frac{1}{2}=0.5$$

Steps Using Definition of Logarithm

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

$$4^{3w}-5=3$$

Add 5 to both sides of the equation.

$$4^{3w}=8$$

Take the logarithm of both sides of the equation.

$$\log(4^{3w})=\log(8)$$

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

$$3w\log(4)=\log(8)$$

Divide both sides by \log(4).

$$3w=\frac{\log(8)}{\log(4)}$$

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

$$3w=\log_{4}\left(8\right)$$

Divide both sides by 3.

$$w=\frac{\frac{3}{2}}{3}$$