What is the value of log eight to the base two?
To answer this question, we recall that logarithms are the opposite or inverse of exponentials. 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. In this question, our value of 𝑎 is two, our value of 𝑏 is eight, and we want to calculate 𝑐.
Substituting in these values gives us two to the power of 𝑐 is equal to eight. 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. As our value of 𝑐 is equal to three, we can conclude that log eight to the base two equals three.