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Logarithmic Properties

对数的基本运算性质

loga​(xy)=loga​x+loga​yandloga​(yx​)=loga​x−loga​y

Theoretical Identity Description:

Core operational laws of logarithmic functions: the log of a product is the sum of the logs, and the log of a quotient is the difference of the logs.

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Rigorous Derivation Tree

2 Logical Steps
Step 1check_circleValid Deduction
loga​(xy)=loga​x+loga​yandloga​(yx​)=loga​x−loga​y

Foundational identity statement defined under standard mathematical conditions.

Step 2check_circleValid Deduction
loga​(xy)=loga​x+loga​y

Targeted algebraic evaluation and parameter substitution.

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CSCA Exam Triggers & Traps

High-Yield Exam Focus
psychologyProblem Pattern Recognition

Apply whenever an exam question presents conditions matching this canonical identity.

errorCommon Examination Pitfalls

Be vigilant of domain boundaries, sign flips, and degenerate boundary condition cases.

Authentic CBT Past-Paper Questions

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Related Formulas in Functions

6 Formulas
Change of Base Formula
对数的换底公式
Logarithmic Properties
对数的基本运算性质
Trigonometric Pythagorean Identity
同角三角关系(平方关系)
Double-Angle Formula (Sine)
正弦的二倍角公式
Double-Angle Formula (Cosine)
余弦的二倍角公式
Function Parity (Odd & Even)
函数的奇偶性

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