Exercises for Question Type 4: Using logarithms to solve simple exponential equations

Question 1

Skill question

Solve for $x$ in the equation $7^{2 x} = 4 9^{x + 1}$ .

[5]

Question 2

Skill question

Solve for $x$ in the equation $2^{3 x - 1} = 5^{x + 2}$ . Give your answer in exact form.

[4]

Question 3

Skill question

Solve for $x$ in the equation $2^{x + 2} = 5^{1 - x}$ .

[4]

Question 4

Skill question

Solve for $x$ in the equation $3^{x - 4} = 7$ .

[3]

Question 5

Skill question

Solve for $x$ in the equation $1 0^{x} = 3.56$ .

[2]

Question 6

Skill question

Solve for $x$ in the equation $e^{2 x} = 10$ .

[3]

Question 7

Skill question

Solve for $x$ in the equation $5^{2 x + 1} = 125$ .

[3]

Question 8

Skill question

Solve for $x$ in the equation $3^{2 x + 1} = \frac{1}{9}$ .

[3]

Question 9

Skill question

Solve for $x$ in the equation $2^{x} = 23$ .

[3]

Question 10

Skill question

Solve for $x$ in the equation $(\frac{1}{2})^{x} = 16$ .

[2]

Question 11

Skill question

Solve for $x$ in the equation $4^{x + 1} = 8^{2 x - 1}$ .

[4]

Question 12

Skill question

Solve for $x$ in the equation $9^{x} = 2 7^{x - 2}$ .

[3]

IB Mathematics Applications & Interpretation Question Type 4: Using Logarithms to Solve Simple Exponential Equations Exercises