Question Video: Solving Exponential Equations Using Laws of Exponents Mathematics • Second Year of Secondary School

Video Transcript

Given that three to the power of 𝑥 plus two is equal to 81, find the value of 𝑥.

We can begin here by recognizing that 81 is equal to three to the fourth power. This means that we can rewrite our equation as three to the power of 𝑥 plus two is equal to three to the power of four. As the base value on both sides is three, the exponents must be equal. 𝑥 plus two must be equal to four. We can subtract two from both sides of this equation, giving us 𝑥 is equal to two. The value of 𝑥 that satisfies the equation three to the power of 𝑥 plus two equals 81 is two.