WEBVTT
00:00:02.080 --> 00:00:05.600
What is the value of log eight to the base two?
00:00:06.880 --> 00:00:12.880
To answer this question, we recall that logarithms are the opposite or inverse of exponentials.
00:00:13.680 --> 00:00:21.680
This means that if log 𝑏 to the base 𝑎 is equal to 𝑐, then 𝑎 to the power of 𝑐 is equal to 𝑏.
00:00:22.560 --> 00:00:30.560
In this question, our value of 𝑎 is two, our value of 𝑏 is eight, and we want to calculate 𝑐.
00:00:31.840 --> 00:00:36.960
Substituting in these values gives us two to the power of 𝑐 is equal to eight.
00:00:37.920 --> 00:00:48.320
We know that two cubed or two to the power of three is equal to eight, as two multiplied by two multiplied by two equals eight.
00:00:49.120 --> 00:00:57.960
As our value of 𝑐 is equal to three, we can conclude that log eight to the base two equals three.