Last updated on Sep 22, 2026

Logarithm Laws and Properties (HSC SSCE Mathematics Advanced): Flashcards

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Logarithm Laws and Properties

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Logarithms are the inverse of what type of functions?

Exponential functions

$\log_a(a^x) = ?$

$x$

$a^{\log_a(x)} = ?$

$x$

$\log_a(a) = ?$

$1$

$\log_a(1) = ?$

$0$

$\log_a(\frac{1}{x}) = ?$

$-\log_a(x)$

$\log_a(xy) = ?$ (product law)

$\log_a(x) + \log_a(y)$

$\log_a(\frac{x}{y}) = ?$ (quotient law)

$\log_a(x) - \log_a(y)$

$\log_a(x^n) = ?$ (power law)

$n\log_a(x)$

Product law transforms multiplication into what operation?

Addition

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Logarithm Laws and Properties (HSC SSCE Mathematics Advanced): Flashcards

Practise the cards

Logarithms are the inverse of what type of functions?

log⁡a(ax)=?\log_a(a^x) = ?loga​(ax)=?

alog⁡a(x)=?a^{\log_a(x)} = ?aloga​(x)=?

log⁡a(a)=?\log_a(a) = ?loga​(a)=?

log⁡a(1)=?\log_a(1) = ?loga​(1)=?

log⁡a(1x)=?\log_a(\frac{1}{x}) = ?loga​(x1​)=?

log⁡a(xy)=?\log_a(xy) = ?loga​(xy)=? (product law)

log⁡a(xy)=?\log_a(\frac{x}{y}) = ?loga​(yx​)=? (quotient law)

log⁡a(xn)=?\log_a(x^n) = ?loga​(xn)=? (power law)

Product law transforms multiplication into what operation?

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Quizzes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

$\log_a(a^x) = ?$

$a^{\log_a(x)} = ?$

$\log_a(a) = ?$

$\log_a(1) = ?$

$\log_a(\frac{1}{x}) = ?$

$\log_a(xy) = ?$ (product law)

$\log_a(\frac{x}{y}) = ?$ (quotient law)

$\log_a(x^n) = ?$ (power law)