Solve 0.3=2^a

$$0.3 = 2 ^ { a }$$

Solve for a

$$a=\log_{2}\left(0.3\right)\approx -1.736965594$$

Steps Using Definition of Logarithm

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

$$2^{a}=0.3$$

Take the logarithm of both sides of the equation.

$$\log(2^{a})=\log(0.3)$$

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

$$a\log(2)=\log(0.3)$$

Divide both sides by \log(2).

$$a=\frac{\log(0.3)}{\log(2)}$$

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

$$a=\log_{2}\left(0.3\right)$$