Last updated on Sep 22, 2026

Logarithms (HSC SSCE Mathematics Advanced): Quizzes

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Logarithms

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What does $\log_a(x) = y$ represent?

The exponent $y$ such that $a^y = x$

Which constraint applies to the base $a$ in $\log_a(x)$ ?

$a > 0$ and $a \neq 1$

Which constraint applies to the argument $x$ in $\log_a(x)$ ?

$x > 0$

What is $10^2 = 100$ written in logarithmic form?

$\log(100) = 2$

What is $\log_3(81) = 4$ written in exponential form?

$3^4 = 81$

What is the value of $\log_2(8)$ ?

$3$

When $\log(x)$ is written without a subscript, what base does it use?

Base 10

What is the base of the natural logarithm $\ln(x)$ ?

$e \approx 2.71828$

Which inverse property is correct for natural logarithms?

$e^{\ln(x)} = x$ where $x > 0$

What is the value of $\log_5\left(\frac{1}{25}\right)$ ?

$-2$

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Logarithms (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

What does log⁡a(x)=y\log_a(x) = yloga​(x)=y represent?

Which constraint applies to the base aaa in log⁡a(x)\log_a(x)loga​(x)?

Which constraint applies to the argument xxx in log⁡a(x)\log_a(x)loga​(x)?

What is 102=10010^2 = 100102=100 written in logarithmic form?

What is log⁡3(81)=4\log_3(81) = 4log3​(81)=4 written in exponential form?

What is the value of log⁡2(8)\log_2(8)log2​(8)?

When log⁡(x)\log(x)log(x) is written without a subscript, what base does it use?

What is the base of the natural logarithm ln⁡(x)\ln(x)ln(x)?

Which inverse property is correct for natural logarithms?

What is the value of log⁡5(125)\log_5\left(\frac{1}{25}\right)log5​(251​)?

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

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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 does $\log_a(x) = y$ represent?

Which constraint applies to the base $a$ in $\log_a(x)$ ?

Which constraint applies to the argument $x$ in $\log_a(x)$ ?

What is $10^2 = 100$ written in logarithmic form?

What is $\log_3(81) = 4$ written in exponential form?

What is the value of $\log_2(8)$ ?

When $\log(x)$ is written without a subscript, what base does it use?

What is the base of the natural logarithm $\ln(x)$ ?

What is the value of $\log_5\left(\frac{1}{25}\right)$ ?