How many practice questions are available for Logarithms?

SparkEd Math offers 60+ practice questions for Logarithms across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Logarithms content free on SparkEd Math?

Yes! All Logarithms content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Logarithms differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Logarithms problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Logarithms content aligned with the IB syllabus?

Yes, all Logarithms questions and lessons on SparkEd Math are fully aligned with the International Baccalaureate (MYP) (IB) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Logarithms — Class 9 IB (2025-26)

About Logarithms — Class 9 IB

Define logarithms, apply laws of logarithms, and solve exponential equations. This topic is part of the IB Class 9 mathematics syllabus (chapter: Unit 12). On this page you can practice 59 questions across three difficulty levels — 20 easy, 19 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Logarithms — solved examples for Class 9 IB

Example 1easy

Convert the exponential equation 5^3 = 125 into its equivalent logarithmic form.

A)log_3(125) = 5
B)log_5(3) = 125
C)log_125(5) = 3
D)log_5(125) = 3

Step-by-step solution

The general definition of a logarithm states that if b^c = a, then log_b(a) = c.
In the given exponential equation, 5^3 = 125, we have the base b = 5, the exponent c = 3, and the result a = 125.
Applying the definition, we convert it to log_5(125) = 3.

Answer: log_5(125) = 3

Example 2medium

If 7^y = 343, which of the following logarithmic equations correctly represents the value of y?

A)log_343(7) = y
B)log_7(y) = 343
C)log_y(343) = 7
D)log_7(343) = y

Step-by-step solution

The definition of a logarithm states that if an exponential equation is given as b^x = N, it can be rewritten in logarithmic form as log_b(N) = x.
In the given equation, 7^y = 343, we have b = 7, x = y, and N = 343.
Applying the definition, the logarithmic form will be log_7(343) = y.

Answer: log_7(343) = y

Example 3hard

Which of the following statements about logarithms is always true for any real numbers a, b, and x?

A)log_b(a) is defined for any a > 0.
B)log_b(a) is defined for any b ≠ 1.
C)log_b(a) is defined only when a > 0, b > 0, and b ≠ 1.
D)log_b(a) is defined for all a and b.

Step-by-step solution

The definition of a logarithm, log_b(a) = x if and only if b^x = a, imposes specific conditions on 'a' and 'b'.
For b^x to consistently map to positive values 'a' and to avoid undefined cases, the base 'b' must be positive (b > 0) and not equal to 1 (b ≠ 1).
$b > 0, b ≠ 1$
Consequently, the argument 'a' must always be positive (a > 0), as a positive base raised to any real power will always yield a positive result.
$a > 0$
Therefore, the statement 'log_b(a) is defined only when a > 0, b > 0, and b ≠ 1' is the only one that is always true.

Answer: log_b(a) is defined only when a > 0, b > 0, and b ≠ 1.

Practice questions on Logarithms

Q1.easy
Which of the following statements correctly explains why log_7(1) = 0?
1. A)Because 7^0 = 1, and the logarithm is the exponent.
2. B)Because 7 × 0 = 1, and logarithms are about multiplication.
3. C)Because 7 ÷ 1 = 7, and logarithms are about division.
4. D)Because 7 + 0 = 7, and logarithms are about addition.
Show answer
Answer: Because 7^0 = 1, and the logarithm is the exponent.
Hint: Recall the definition of a logarithm: log_b(a) = c means b^c = a. What power of any number (except 0) gives 1?
Q2.easy
A student claimed that log_9(9) = 9. Identify the mistake in their reasoning.
1. A)The base of the logarithm should be 1, not 9.
2. B)log_9(9) equals 1, because 9 raised to the power of 1 gives 9.
3. C)log_9(9) equals 0, because any number raised to the power of 0 is 1.
4. D)The number inside the logarithm must be different from the base.
Show answer
Answer: log_9(9) equals 1, because 9 raised to the power of 1 gives 9.
Hint: Think about what exponent you would put on the base to get the number inside the logarithm.
Q3.easy
Evaluate log_4(64).
1. A)2
2. B)3
3. C)4
4. D)16
Show answer
Answer: 3
Hint: Ask yourself: 'What power must 4 be raised to in order to get 64?'
Q4.medium
Simplify the expression: log(x^3 y^2 / z^4), assuming base 10.
1. A)3log(x) + 2log(y) + 4log(z)
2. B)3log(x) + 2log(y) - 4log(z)
3. C)log(x^3) + log(y^2) / log(z^4)
4. D)log(x) + log(y) - log(z)
Show answer
Answer: 3log(x) + 2log(y) - 4log(z)
Hint: Apply the product, quotient, and power rules of logarithms step-by-step. Remember that division implies subtraction of logarithms.
Q5.medium
Evaluate the expression: log_2(16) + log_3(1/27) - log_5(√5).
1. A)4
2. B)0.5
3. C)-0.5
4. D)1.5
Show answer
Answer: 0.5
Hint: Express each number as a power of its base. Remember that 1/a^n = a^(-n) and √a = a^(1/2).
Q6.medium
Solve for x: 5^(x-2) = 125.
1. A)x = 3
2. B)x = 4
3. C)x = 5
4. D)x = 25
Show answer
Answer: x = 5
Hint: Try to express both sides of the equation with the same base. Recognize that 125 is a power of 5.
Q7.hard
Simplify the expression: 3 × log_2(16) + 2 × log_3(1/9) - log_5(√125).
1. A)10
2. B)5
3. C)0
4. D)-1
Show answer
Answer: 5
Hint: Convert each term into a simpler logarithmic form using the definition and properties, then evaluate the logarithms individually.
Q8.hard
If 7^(x-1) = 3^(2x+1), find the value of x correct to two decimal places.
1. A)1.34
2. B)-1.34
3. C)0.87
4. D)-0.87
Show answer
Answer: -0.87
Hint: Take the logarithm of both sides of the equation to bring down the exponents. Remember to use the power rule of logarithms.
Q9.hard
Given that log_b(a) = X and log_b(c) = Y, show that log_b( (a^3 × c) / b^2 ) can be expressed as 3X + Y - 2.
1. A)The statement is always true.
2. B)The statement is true only if b = 10.
3. C)The statement is false, the correct expression is 3X + Y + 2.
4. D)The statement is false, the correct expression is (3X + Y) / 2.
Show answer
Answer: The statement is always true.
Hint: Apply the logarithm laws for product, quotient, and power, and remember the value of log_b(b).

These are 9 of the 59 questions available for Logarithms. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.