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

Video Transcript

Use the calculator to find the value of 𝑥 for which nine to the power of 𝑥 equals eight. Give your answer to two decimal places.

In order to solve this problem, we’ll use the property that if 𝑎 to the power of 𝑥 is equal to 𝑏, then 𝑥 is equal to log 𝑏 to the base 𝑎. In our case, we’re asked to solve nine to the power of 𝑥 equals eight. This means that 𝑥 is equal to log eight to the base nine. Typing this into the calculator gives us a value of 𝑥 of 0.95 to two decimal places.

This means that nine to the power of 0.95 is equal to eight.