Solve 2^a+frac{10{3}}=18

$$2 ^ { a + \frac { 10 } { 3 } } = 18$$

Solve for a

$$a=2\log_{2}\left(3\right)-\frac{7}{3}\approx 0.836591668$$

Steps Using Definition of Logarithm

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

$$2^{a+\frac{10}{3}}=18$$

Take the logarithm of both sides of the equation.

$$\log(2^{a+\frac{10}{3}})=\log(18)$$

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

$$\left(a+\frac{10}{3}\right)\log(2)=\log(18)$$

Divide both sides by \log(2).

$$a+\frac{10}{3}=\frac{\log(18)}{\log(2)}$$

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

$$a+\frac{10}{3}=\log_{2}\left(18\right)$$

Subtract \frac{10}{3} from both sides of the equation.

$$a=\log_{2}\left(18\right)-\frac{10}{3}$$