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SL 1.5—Intro to logs - IB Questionbank | RevisionDojo

Practice SL 1.5—Intro to logs with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SL & HLPaper 1

Given that $\log_2 p = m$ and $\log_{\sqrt{2}} q = n$ , express $\frac{p^2}{q}$ as a power of 2.

Express $\frac{p^2}{q}$ as a power of 2.

[4]

Question 2

SL & HLPaper 1

Evaluate the expression, without using a calculator:

$2 \log_3 6 - \log_3 4 + \log_3 \left(\frac{1}{9}\right)$

[4]

Question 3

SL & HLPaper 1

Check whether the logarithm $\log_3 (7 - 3x)$ is defined for each of the following:

$x = 1$

[1]

$x = 2$

[1]

Question 4

SL & HLPaper 1

Given that $\log_4 a = m$ and $\log_8 (2a) = n$ , show that $2m = 3n - 1$ .

[4]

Question 5

SL & HLPaper 1

Given the system of equations:

$\log_2 x - \log_4 y = 1$

$\log_8 x + \log_2 y = 2$

Solve for $x$ and $y$ .

[7]

Question 6

SL & HLPaper 1

Convert the following to index form:

$4 = \log_3 81$

[2]

$3 = \log_{10} 1000$

[2]

$\frac{1}{3} = \log_8 2$

[2]

Question 7

SL & HLPaper 1

Prove that if $x, y, z$ are positive real numbers such that $x^a y^b z^c = 1$ , then $\frac{a}{\log_x k} + \frac{b}{\log_y k} + \frac{c}{\log_z k} = 0$ for any positive real number $k \ne 1$ .

[5]

Question 8

SL & HLPaper 1

Solve the equation $\log_2 (3x - 5) + \frac{3}{\log_2 (3x - 5)} = 4$ , given that $3x - 5 > 0$ .

[5]

Question 9

SL & HLPaper 1

Solve the following equations:

$\log_2 x = 3$

[2]

$\log_5 (2x - 1) = 2$

[2]

Question 10

SLPaper 1

A local environmental organization is studying the growth of a particular plant species in relation to its nutrient uptake. They have modeled the nutrient uptake function as $f(x) = \log_2(x + 1) + \log_2(x - 3)$ , where $x$ represents the amount of water (in liters) supplied to the plants.

Show that $f(x)$ can be simplified to a single logarithmic expression.

[3]

Hence, or otherwise, solve $\log_2(x + 1) + \log_2(x - 3) = 5$ .

[3]

SL 1.5—Intro to logs Questionbank