Video Transcript
Consider the function 𝑓 of 𝑥 is equal to log base three of 𝑥. Find the value of 𝑓 of nine.
In this question, we are given the logarithmic function log base three of 𝑥. And we want to calculate this when 𝑥 is equal to nine. 𝑓 of nine is therefore equal to log base three of nine. We recall that a logarithmic function is the inverse of an exponential function. If 𝑦 is equal to log base 𝑎 of 𝑥, then 𝑥 is equal to 𝑎 of 𝑦.
In this question, we will let the value we are trying to calculate be 𝑦 such that 𝑦 is equal to log base three of nine. This can be rewritten as three to the power of 𝑦 is equal to nine. Since three squared is equal to nine, we know that 𝑦 is equal to two.
If 𝑓 of 𝑥 is equal to log base three of 𝑥, then 𝑓 of nine equals two.
