Solve 3^a+3=1

$${ 3 }^{ a+3 } = 1$$

Solve for a

$$a=-3$$

Steps Using Definition of Logarithm

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

$$3^{a+3}=1$$

Take the logarithm of both sides of the equation.

$$\log(3^{a+3})=\log(1)$$

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

$$\left(a+3\right)\log(3)=\log(1)$$

Divide both sides by \log(3).

$$a+3=\frac{\log(1)}{\log(3)}$$

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

$$a+3=\log_{3}\left(1\right)$$

Subtract 3 from both sides of the equation.

$$a=-3$$