Exercises for Question Type 2: Using logarithm laws to simplify algebraic expressions into a single term

Question 1

Skill question

Simplify $lo g_{2} (x^{3}) - 4 lo g_{2} (x)$ into a single logarithm.

[3]

Question 2

Skill question

Simplify $lo g_{b} (a) + lo g_{b} (b^{2}) - 2 lo g_{b} (a^{2})$ into a single logarithm.

[3]

Question 3

Skill question

Simplify $lo g_{5} (25) + 3 lo g_{5} (2) - lo g_{5} (4)$ into a single logarithm.

[4]

Question 4

Skill question

Simplify $2 lo g_{7} (14) - lo g_{7} (2)$ into a single logarithm.

[3]

Question 5

Skill question

Properties of logarithms

Simplify $4 lo g_{4} (x) - 2 lo g_{4} (x)$ into a single logarithm.

[3]

Question 6

Skill question

Simplify $3 lo g_{3} (2) - 2 lo g_{3} (5)$ into a single logarithm.

[2]

Question 7

Skill question

Simplify $lo g_{3} (x) + lo g_{3} (2) - 3 lo g_{3} (6)$ into a single logarithm.

[4]

Question 8

Skill question

Simplify $2 lo g_{2} (x + 1) - lo g_{2} (4 (x + 1)^{2})$ into a single logarithm.

[3]

Question 9

Skill question

Properties of logarithms

Simplify $5 lo g_{k} (m) + lo g_{k} (n) - 2 lo g_{k} (p)$ into a single logarithm.

[3]

Question 10

Skill question

Logarithms

Simplify $lo g_{x} (y) - 4 lo g_{x} (2 y)$ into a single logarithm.

[3]

Question 11

Skill question

Simplify the expression $lo g_{a} (x) + 2 lo g_{a} (y) - lo g_{a} (z)$ into a single logarithm.

[3]

IB Mathematics Applications & Interpretation Question Type 2: Using Logarithm Laws to Simplify Algebraic Expressions Into a Single Term Exercises