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Logarithms and Non-Linear Inequalities - MYP Questionbank | RevisionDojo

Practice Logarithms and Non-Linear Inequalities with authentic MYP MYP Extended Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

Solve for $k$ in the equation: $\log_k \sqrt{27} = \frac{3}{4}$

Question 2

True or False: The identity $\frac{\log_a M}{\log_a N} = \log_a (M-N)$ is a valid logarithm law for all $M > N > 0$ .

Question 3

Consider the inequality $y > \ln(4 - x)$ . What is the primary domain restriction that must be reflected in the shaded solution region?

Question 4

Rewrite the expression $1 + 2\log_a x$ as a single logarithm with base $a$ .

Question 5

If $u = \ln x$ and $v = \ln y$ , express $\ln \left( \frac{\sqrt{x}}{y^3} \right)$ in terms of $u$ and $v$ .

Question 6

Expand the expression $\log_a \left( \frac{a^3}{x} \right)$ into its simplest form using logarithm laws.

Question 7

Solve the following exponential equation for $x$ :

2^{3x} \cdot 4^x = 32

Question 8

True or False: The point $(-3, 10)$ is part of the solution region for the inequality $y \ge x^2 + 2$ .

Question 9

Solve for $x$ in the equation $\log_2 x + \log_4 x = 3$ .

Question 10

True or False: The point $(0,0)$ can be used as a valid test point to determine the shading region for the inequality $y > x^2 + x$ .

Type

Difficulty

Question 1

Solve for $k$ in the equation: $\log_k \sqrt{27} = \frac{3}{4}$

Question 2

True or False: The identity $\frac{\log_a M}{\log_a N} = \log_a (M-N)$ is a valid logarithm law for all $M > N > 0$ .

Question 3

Consider the inequality $y > \ln(4 - x)$ . What is the primary domain restriction that must be reflected in the shaded solution region?

Question 4

Rewrite the expression $1 + 2\log_a x$ as a single logarithm with base $a$ .

Question 5

If $u = \ln x$ and $v = \ln y$ , express $\ln \left( \frac{\sqrt{x}}{y^3} \right)$ in terms of $u$ and $v$ .

Question 6

Expand the expression $\log_a \left( \frac{a^3}{x} \right)$ into its simplest form using logarithm laws.

Question 7

Solve the following exponential equation for $x$ :

2^{3x} \cdot 4^x = 32

Question 8

True or False: The point $(-3, 10)$ is part of the solution region for the inequality $y \ge x^2 + 2$ .

Question 9

Solve for $x$ in the equation $\log_2 x + \log_4 x = 3$ .

Question 10

True or False: The point $(0,0)$ can be used as a valid test point to determine the shading region for the inequality $y > x^2 + x$ .

Type

Difficulty

Question 1

Solve for $k$ in the equation: $\log_k \sqrt{27} = \frac{3}{4}$

Question 2

True or False: The identity $\frac{\log_a M}{\log_a N} = \log_a (M-N)$ is a valid logarithm law for all $M > N > 0$ .

Question 3

Consider the inequality $y > \ln(4 - x)$ . What is the primary domain restriction that must be reflected in the shaded solution region?

Question 4

Rewrite the expression $1 + 2\log_a x$ as a single logarithm with base $a$ .

Question 5

If $u = \ln x$ and $v = \ln y$ , express $\ln \left( \frac{\sqrt{x}}{y^3} \right)$ in terms of $u$ and $v$ .

Question 6

Expand the expression $\log_a \left( \frac{a^3}{x} \right)$ into its simplest form using logarithm laws.

Question 7

Solve the following exponential equation for $x$ :

2^{3x} \cdot 4^x = 32

Question 8

True or False: The point $(-3, 10)$ is part of the solution region for the inequality $y \ge x^2 + 2$ .

Question 9

Solve for $x$ in the equation $\log_2 x + \log_4 x = 3$ .

Question 10

True or False: The point $(0,0)$ can be used as a valid test point to determine the shading region for the inequality $y > x^2 + x$ .

Logarithms and Non-Linear Inequalities Questionbank