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SL 1.7—Laws of exponents and logs - IB Questionbank | RevisionDojo

Practice SL 1.7—Laws of exponents and 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

Simplify the following, leaving your answers in the form $a^k$ :

$27^{\frac{1}{3}} \times 9^{\frac{1}{2}}$

[3]

$\frac{125^{\frac{2}{3}}}{5^{\frac{1}{2}}}$

[3]

Question 2

SL & HLPaper 1

If $A \left(\frac{x^2}{3}\right) \left(\frac{9}{x}\right)^k$ can be simplified to $x^3$ ,

find the values of the constants $A$ and $k$ .

[6]

Question 3

SL & HLPaper 1

By rationalizing the denominators, simplify the following:

$\frac{15}{2\sqrt{5}}$

[2]

$\frac{\sqrt{7} + \sqrt{3}}{\sqrt{7} - \sqrt{3}}$

[4]

Question 4

SL & HLPaper 1

Solve the following simultaneous equations:

$\begin{cases} 2^x = y \\ \log_y 64 = 3 \end{cases}$

[4]

$\begin{cases} {\log_2 x + \log_2 y = 5} \\ {\log_2 x - \log_2 y = 1} \end{cases}$

[5]

Question 5

SL & HLPaper 1

Solve the simultaneous equations:

$\begin{cases} 9^{x+1} = 27^{y+2} \quad (1) \\ 2^{x+y} = 16 \quad (2) \end{cases}$

[7]

Question 6

SL & HLPaper 1

Solve the following equation:

$2 \log_7 x = \log_7 36$

[3]

Question 7

SL & HLPaper 1

Solve the following equation:

$\log_2 (x+1) + \log_2 (x-1) = 3$

[5]

Question 8

SL & HLPaper 1

Solve the following equation:

$4^{2x+1} = \frac{1}{32^x}$

[4]

Question 9

SLPaper 1

A researcher is studying the effects of a new agricultural technique on crop yield. The yield can be represented by the expression $(16 x^4 y^{-2})^{\frac{1}{4}}$ .

Simplify this expression to understand the yield per unit area.

[3]

Question 10

SLPaper 1

A data analyst is working with exponential growth models and needs to convert the equation representing a growth scenario, $5^x=125$ , into logarithmic form to solve for the variable $x$ .

Rewrite the equation in logarithmic form and solve for $x$ .

[2]

SL 1.7—Laws of exponents and logs Questionbank