Video Transcript
Solve 13.5 to the power of 𝑥 is equal to 5.6, giving your answer to the nearest two decimal places.
In this question, we are given an exponential equation in the form 𝑎 to the power of 𝑥 is equal to 𝑏. Since a logarithmic function is the inverse of an exponential function, we know that if 𝑎 to the power of 𝑥 equals 𝑏, then 𝑥 is equal to log base 𝑎 of 𝑏.
In this question, we can rewrite our equation as 𝑥 is equal to log base 13.5 of 5.6. Typing this into the calculator gives us 0.661917 and so on. We are asked to give our answer to the nearest two decimal places. And since the one in the thousandths column is less than five, we round down.
The solution to the equation 13.5 to the power of 𝑥 equals 5.6 is 𝑥 is equal to 0.66. We can check this answer by typing 13.5 to the power of 0.66 and so on into our calculator. Using the exact value gives us an answer of 5.6. This proves that our value of 𝑥 0.66 to two decimal places is correct. Had we used the approximated value in our check, our answer would have been approximately 5.6.
