Video Transcript
Find the solution set of the equation log base five of 125 is equal to 𝑥 plus one.
In this question, the left-hand side of our equation is a logarithmic expression. And we know that a logarithmic function is the inverse of an exponential function. If 𝑦 is equal to log base 𝑎 of 𝑏, then 𝑏 is equal to 𝑎 to the power of 𝑦, where 𝑎 and 𝑏 are positive numbers and 𝑎 is not equal to one.
In this question, we will let 𝑦 equal log base five of 125. This means that 125 is equal to five to the power of 𝑦. We know that five cubed is equal to 125. Therefore, 𝑦 is equal to three. Log base five of 125 equals three. Going back to our original equation, this means that 𝑥 plus one must equal three. Subtracting one from both sides of this equation, we have 𝑥 is equal to two. The solution set of the equation log base five of 125 equals 𝑥 plus one is the number two.