Exercises for Question Type 10: Summarizing laws of logarithms

Question 1

Skill question

Expand $lo g_{3} (27 x^{2})$ .

[3]

Question 2

Skill question

Expand $ln (\frac{e ^{3} x}{y})$ .

[3]

Question 3

Skill question

Expand $lo g_{7} (\frac{x y}{z ^{3}})$ .

[3]

Question 4

Skill question

Solve $2 + lo g_{4} (x) = ln (x)$ for $x > 0$ .

[5]

Question 5

Skill question

Express $lo g_{a} (b)$ in terms of natural logarithms.

[1]

Question 6

Skill question

Solve the following equation.

Solve $ln (x^{2} - 1) - ln (x + 1) = ln (2)$ for $x$ . [4 marks]

[4]

Question 7

Skill question

Evaluate logarithmic expressions using change of base rules.

Evaluate $lo g_{4} (32)$ by rewriting in base 2. [3 marks]

[3]

Question 8

Skill question

Solve $lo g_{5} (x) + lo g_{5} (x - 4) = 1$ for $x$ .

[5]

Question 9

Skill question

Solve the logarithmic equation.

Solve $lo g_{3} (2 x - 1) = 2 + lo g_{3} (x + 1)$ for $x$ .

[7]

Question 10

Skill question

Condense $4 + lo g_{5} (x) - 2 lo g_{5} (y)$ into one logarithm.

[4]

Question 11

Skill question

Express $lo g_{2} (x) + 3 lo g_{2} (y) - \frac{1}{2} lo g_{2} (z)$ as a single logarithm.

[2]

Question 12

Skill question

Solve $lo g_{2} (x^{2} - 4) = 3$ for $x$ .

[3]

IB Mathematics Analysis and Approaches Question Type 10: Summarizing Laws of Logarithms Exercises