Exercises for Question Type 1: Using logarithm laws to solve numerical expressions

Question 1

Skill question

Evaluate a numerical expression involving logarithms with different bases using properties of logarithms and the change of base formula.

Compute $(lo g_{2} 16 - lo g_{8} 2) + lo g_{4} 4$ .

[6]

Question 2

Skill question

Find the value of $3 lo g_{5} 25 - lo g_{5} 125$ .

[3]

Question 3

Skill question

Logarithms and their properties.

Simplify the following expression:

$2 lo g_{7} 49 - lo g_{7} 7 + lo g_{7} 14$

[4]

Question 4

Skill question

Evaluating logarithmic expressions using base 10 properties and log laws.

Evaluate $(lo g_{10} 1000 - lo g_{10} 10) + lo g_{10} 5$ .

[3]

Question 5

Skill question

Evaluate $(lo g_{3} 81 + 2 lo g_{3} 3) - lo g_{3} 9$ .

[3]

Question 6

Skill question

Simplify $lo g_{4} 32 + lo g_{4} 8 - 3 lo g_{4} 2$ .

[4]

Question 7

Skill question

Simplify $lo g_{5} 125 - 2 lo g_{25} 5 + lo g_{5} \frac{1}{25}$ .

[5]

Question 8

Skill question

Compute $(lo g_{8} 64 + 2 lo g_{4} 2) - lo g_{2} 16$ .

[3]

Question 9

Skill question

Simplify and evaluate $lo g_{2} 8 + lo g_{2} \frac{1}{4} - lo g_{2} 2$ .

[2]

Question 10

Skill question

Find the value of $(lo g_{3} 27 - lo g_{9} 3) + lo g_{3} 3$ .

[5]

Question 11

Skill question

Find the value of $(lo g_{2} 3 + lo g_{2} 6) - lo g_{2} 9$ .

[3]

Question 12

Skill question

Evaluate $2 lo g_{3} 9 + lo g_{9} 3 - lo g_{3} \frac{1}{3}$ .

[5]

IB Mathematics Applications & Interpretation Question Type 1: Using Logarithm Laws to Solve Numerical Expressions Exercises