Exercises for Question Type 3: Using standard logarithms to rewrite expressions

Question 1

Skill question

Simplify $lo g_{7} (49) + 1$ into a single logarithm (base 7).

[3]

Question 2

Skill question

Express $3 + lo g_{x} (y)$ as a single logarithm with base $x$ .

[3]

Question 3

Skill question

Simplify the expression $1 - lo g_{2} (8)$ as a single base- $2$ logarithm.

[3]

Question 4

Skill question

Express $3 + lo g_{10} (x)$ as a single base- $10$ logarithm.

[2]

Question 5

Skill question

Combine $4 + lo g_{4} (7)$ into a single logarithm (base 4).

[3]

Question 6

Skill question

Simplify a logarithmic expression using its properties.

Simplify the expression $2 - lo g_{3} (9)$ using logarithm properties.

[2]

Question 7

Skill question

Logarithmic laws and identities.

Express $5 + lo g_{5} (2)$ as a single logarithm with base 5.

[3]

Question 8

Skill question

Rewrite $lo g_{5} (1) + 3$ as a single base- $5$ logarithm.

[2]

Question 9

Skill question

Simplify the expression $3 + lo g_{2} (5)$ as a single logarithm.

[3]

Question 10

Skill question

Combine $2 + lo g_{3} (5)$ into a single logarithm (base 3).

[3]

Question 11

Skill question

Simplify $- 1 + lo g_{2} (4)$ as a single logarithm (base 2).

[2]

Question 12

Skill question

Simplify $\frac{1}{2} + lo g_{10} (4)$ as a single base-10 logarithm.

[2]

IB Mathematics Applications & Interpretation Question Type 3: Using Standard Logarithms to Rewrite Expressions Exercises