Simplifying Log Expression

追加: 2026-05-17

[00:00:01]Hi, this is your math guru. To simplify the following log expression, I have log to base two of three minus log to base two of 24. Because they have the same base, I'm going to apply the quotient rule, and this becomes log to base two of three over 24.

[00:00:20]If I simplify further, this is log to base two of one over eight. I'm going to change that into exponential form, such that this becomes log to base two of one over two to the power of three, which is log to base two of taking that two negative exponent two to the power of negative three. This becomes negative three log of base two to two.

[00:00:52]Applying the identity rule here, this becomes negative three times one, and my final answer, negative three.