RevisionDojo

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

SL & HLPaper 1

Given that $\log_c 3 = X$ and $\log_c 5 = Y$ .

Evaluate $\log_c 45$ in terms of $X$ and $Y$ .

[3]

Evaluate $\log_c \left(\frac{c^2}{27}\right)$ in terms of $X$ and $Y$ .

[4]

Question 10

SL & HLPaper 1

Given that $5^x = k$ .

Express $5^{x+2}$ in terms of $k$ .

[2]

Express $25^{x-1}$ in terms of $k$ .

[3]

SL 1.7—Laws of exponents and logs Questionbank