Last updated on Oct 10, 2026

Logarithmic Functions (HSC SSCE Mathematics Advanced): Quizzes

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Logarithm Laws and Properties

Practise the questions

10 questions from this quiz

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What is the value of $\log_7(7)$ ?

$1$

What is $\log_{10}(1)$ equal to?

$0$

Simplify $\log_3(3^5)$

$5$

Which property states $\log_a\left(\frac{1}{x}\right) = -\log_a(x)$ ?

Logarithm of a reciprocal

Express $\log_5(20) + \log_5(2)$ as a single logarithm.

$\log_5(40)$

What does $\log_a\left(\frac{x}{y}\right)$ equal?

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

Simplify $3\log_2(8)$ by moving the coefficient inside.

$\log_2(8^3)$

Evaluate $\log_2(32) - \log_2(4)$ completely.

$3$

Logarithms transform multiplication into what operation?

Addition

What is the value of $5^{\log_5(12)}$ ?

$12$

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Logarithmic Functions (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

What is the value of log⁡7(7)\log_7(7)log7​(7)?

What is log⁡10(1)\log_{10}(1)log10​(1) equal to?

Simplify log⁡3(35)\log_3(3^5)log3​(35)

Which property states log⁡a(1x)=−log⁡a(x)\log_a\left(\frac{1}{x}\right) = -\log_a(x)loga​(x1​)=−loga​(x)?

Express log⁡5(20)+log⁡5(2)\log_5(20) + \log_5(2)log5​(20)+log5​(2) as a single logarithm.

What does log⁡a(xy)\log_a\left(\frac{x}{y}\right)loga​(yx​) equal?

Simplify 3log⁡2(8)3\log_2(8)3log2​(8) by moving the coefficient inside.

Evaluate log⁡2(32)−log⁡2(4)\log_2(32) - \log_2(4)log2​(32)−log2​(4) completely.

Logarithms transform multiplication into what operation?

What is the value of 5log⁡5(12)5^{\log_5(12)}5log5​(12)?

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 Flashcards 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

What is the value of $\log_7(7)$ ?

What is $\log_{10}(1)$ equal to?

Simplify $\log_3(3^5)$

Which property states $\log_a\left(\frac{1}{x}\right) = -\log_a(x)$ ?

Express $\log_5(20) + \log_5(2)$ as a single logarithm.

What does $\log_a\left(\frac{x}{y}\right)$ equal?

Simplify $3\log_2(8)$ by moving the coefficient inside.

Evaluate $\log_2(32) - \log_2(4)$ completely.

What is the value of $5^{\log_5(12)}$ ?