To simplify logarithmic expressions with the same base, apply the quotient rule (log_a(x) - log_a(y) = log_a(x/y)), then convert to exponential form and use the identity rule (log_a(a) = 1) to find the final value. For example, log₂(3) - log₂(24) simplifies to log₂(3/24) = log₂(1/8) = log₂(2⁻³) = -3.
Install our extension to search inside any video instantly.
Simplifying Log ExpressionAdded:
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.
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.
Applying the identity rule here, this becomes negative three times one, and my final answer, negative three.
Related Videos
Escaping the Fog
LogicLemurGaming
760 views•2026-06-03
Olympiad Mathematics | Indian | Can You Solve This One?
PhilCoolMath
650 views•2026-06-03
A Brutal Radical Expression Made Easy! The Shortcut Changes Everything.
tamoshop
112 views•2026-06-02
V : jee main /advance class 11 mathematics : Binomial Theorem class-1 ( 29 may 2026 )
dcamclassesiitjeemainsadva9953
125 views•2026-05-29
Is This Pentomino Tileable?
3cycle
241 views•2026-05-30
This Sudoku Has Many Lines!!
CrackingTheCryptic
2K views•2026-05-29
Olympiad Mathematics | Indian Can You Solve This One?
PhilCoolMath
268 views•2026-06-02
Olympiad Mathematics | Indian | Can You Solve This?
PhilCoolMath
669 views•2026-06-02
