Practice AHL 1.9—Log laws with authentic IB Mathematics Applications & Interpretation (AI) 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 IB examiners.
Let . Write the following expressions in terms of and .
Find the value of the integer in each of the following cases:
Consider the properties of logarithms, specifically the product and power rules.
Using the identity , calculate .
If and , find the value of .
Solve the equation . Give your answer in the form , where and are positive integers.
Let and .
Find an expression for in terms of .
Find an expression for in terms of .
Find an expression for in terms of and .
The force, newtons, between two magnets a distance metres apart is modelled by the equation . The following measurements were taken:
Linearize the relationship between and using the given model .
Use linear regression to find the values of and , giving your answer to two significant figures.
The curve $C$ is defined by the equation $xy - \ln y = 1$, $y > 0$.
Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ and $y$.
Determine the equation of the tangent to $C$ at the point $\left( \frac{2}{\mathrm{e}}, \mathrm{e} \right)$.
A computer scientist is analyzing the efficiency of algorithms and uses logarithmic functions to express their performance. In this question, give all answers as integers.
State the value of .
Calculate .
Find .
Consider the expression .
Write the expression in terms of and .
If and , evaluate .
Let and .
Write in terms of and .
Practice AHL 1.9—Log laws with authentic IB Mathematics Applications & Interpretation (AI) 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 IB examiners.
Let . Write the following expressions in terms of and .
Find the value of the integer in each of the following cases:
Consider the properties of logarithms, specifically the product and power rules.
Using the identity , calculate .
If and , find the value of .
Solve the equation . Give your answer in the form , where and are positive integers.
Let and .
Find an expression for in terms of .
Find an expression for in terms of .
Find an expression for in terms of and .
The force, newtons, between two magnets a distance metres apart is modelled by the equation . The following measurements were taken:
Linearize the relationship between and using the given model .
Use linear regression to find the values of and , giving your answer to two significant figures.
The curve $C$ is defined by the equation $xy - \ln y = 1$, $y > 0$.
Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ and $y$.
Determine the equation of the tangent to $C$ at the point $\left( \frac{2}{\mathrm{e}}, \mathrm{e} \right)$.
A computer scientist is analyzing the efficiency of algorithms and uses logarithmic functions to express their performance. In this question, give all answers as integers.
State the value of .
Calculate .
Find .
Consider the expression .
Write the expression in terms of and .
If and , evaluate .
Let and .
Write in terms of and .