Exercises for Question Type 4: Finding logarithm given values for a and b

Question 1

Skill question

Solve for $x$ : $lo g_{3} (9 x) = 3$ .

[2]

Question 2

Skill question

Solve for $x$ : $lo g_{7} (x) = 2$ .

[2]

Question 3

Skill question

Solve for $x$ : $lo g_{10} (x) = - 1$ .

[2]

Question 4

Skill question

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

[3]

Question 5

Skill question

Solve for $x$ : $lo g_{2} (x) = 5$ .

[2]

Question 6

Skill question

Evaluate $lo g_{10} (1000)$ .

[2]

Question 7

Skill question

Simplify $lo g_{7} (7^{4})$ .

[2]

Question 8

Skill question

Solve for $x$ : $lo g_{2} (16) + lo g_{2} (x) = 6$ .

[3]

Question 9

Skill question

Evaluate $lo g_{5} (\frac{1}{25})$ .

[2]

Question 10

Skill question

Evaluate $lo g_{2} (\frac{1}{8})$ .

[2]

Question 11

Skill question

Evaluate $lo g_{3} (27)$ .

[2]

Question 12

Skill question

Solve for $x$ : $lo g_{4} (x) = \frac{3}{2}$ .

[2]

Question 13

Skill question

Solve for $x$ : $lo g (x) + lo g (2) = 3$ , where $lo g$ is base 10.

[3]

Question 14

Skill question

Evaluate $lo g_{4} (64)$ .

[2]

Question 15

Skill question

Evaluate $lo g_{2} (8)$ . [2 marks]

[2]

IB Mathematics Applications & Interpretation Question Type 4: Finding Logarithm Given Values for a and b Exercises