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Logarithms - MYP Questionbank | RevisionDojo

Practice Logarithms 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

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

Question 4

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

Question 5

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

Question 6

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

Question 7

Which of the following expressions is equivalent to $\log_a x + \log_a x + \log_a x$ for all $x > 0$ ?

Question 8

Which of the following is correct regarding the statement $\log_a(x-y) = \frac{\log_a x}{\log_a y}$ for all $a > 0, a \neq 1$ and $x > y > 0$ ?

Question 9

Using the laws of logarithms, expand the following expression completely (assuming $x > -2$ and $y > 0$ ):

\log_a \sqrt{\frac{(x+2)^2}{y^3}}

Question 10

For which set of values for $x$ is the expression $\log_{(x-2)} (5-x)$ mathematically defined?

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

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

Question 4

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

Question 5

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

Question 6

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

Question 7

Which of the following expressions is equivalent to $\log_a x + \log_a x + \log_a x$ for all $x > 0$ ?

Question 8

Which of the following is correct regarding the statement $\log_a(x-y) = \frac{\log_a x}{\log_a y}$ for all $a > 0, a \neq 1$ and $x > y > 0$ ?

Question 9

Using the laws of logarithms, expand the following expression completely (assuming $x > -2$ and $y > 0$ ):

\log_a \sqrt{\frac{(x+2)^2}{y^3}}

Question 10

For which set of values for $x$ is the expression $\log_{(x-2)} (5-x)$ mathematically defined?

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

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

Question 4

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

Question 5

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

Question 6

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

Question 7

Which of the following expressions is equivalent to $\log_a x + \log_a x + \log_a x$ for all $x > 0$ ?

Question 8

Which of the following is correct regarding the statement $\log_a(x-y) = \frac{\log_a x}{\log_a y}$ for all $a > 0, a \neq 1$ and $x > y > 0$ ?

Question 9

Using the laws of logarithms, expand the following expression completely (assuming $x > -2$ and $y > 0$ ):

\log_a \sqrt{\frac{(x+2)^2}{y^3}}

Question 10

For which set of values for $x$ is the expression $\log_{(x-2)} (5-x)$ mathematically defined?

Logarithms Questionbank