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Logarithmic equations - MYP Questionbank | RevisionDojo

Practice Logarithmic equations with authentic MYP MYP Extended Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

Solve the following exponential equation for $x$ :

2^{3x} \cdot 4^x = 32

Question 2

Find the exact solution to the equation $5^x = 12$ .

Question 3

Evaluate $\log_9 27$ without a calculator.

Question 4

Given that $\log_3 5 = k$ , find the value of $\log_9 25$ in terms of $k$ .

Question 5

Solve the logarithmic equation for $x$ : $\log_{2}(x+4) + \log_{2}(x-2) = 4$

Question 6

If $f(x) = \log_5(x-2)$ , find the value of $f^{-1}(2)$ .

Question 7

Solve the logarithmic equation for $x$ :

\log_3 x + \log_3(x-2) = 1

Question 8

Solve the exponential equation for $x$ by writing both sides with the same base:

4^{x+1} = 8^{x-1}

Question 9

Which of the following expressions is equivalent to $\log_2 7$ using the change of base formula?

Question 10

Solve the exponential equation for $x$ :

9^{x-1} = \left(\dfrac{1}{27}\right)^{x+2}

Type

Difficulty

Question 1

Solve the following exponential equation for $x$ :

2^{3x} \cdot 4^x = 32

Question 2

Find the exact solution to the equation $5^x = 12$ .

Question 3

Evaluate $\log_9 27$ without a calculator.

Question 4

Given that $\log_3 5 = k$ , find the value of $\log_9 25$ in terms of $k$ .

Question 5

Solve the logarithmic equation for $x$ : $\log_{2}(x+4) + \log_{2}(x-2) = 4$

Question 6

If $f(x) = \log_5(x-2)$ , find the value of $f^{-1}(2)$ .

Question 7

Solve the logarithmic equation for $x$ :

\log_3 x + \log_3(x-2) = 1

Question 8

Solve the exponential equation for $x$ by writing both sides with the same base:

4^{x+1} = 8^{x-1}

Question 9

Which of the following expressions is equivalent to $\log_2 7$ using the change of base formula?

Question 10

Solve the exponential equation for $x$ :

9^{x-1} = \left(\dfrac{1}{27}\right)^{x+2}

Type

Difficulty

Question 1

Solve the following exponential equation for $x$ :

2^{3x} \cdot 4^x = 32

Question 2

Find the exact solution to the equation $5^x = 12$ .

Question 3

Evaluate $\log_9 27$ without a calculator.

Question 4

Given that $\log_3 5 = k$ , find the value of $\log_9 25$ in terms of $k$ .

Question 5

Solve the logarithmic equation for $x$ : $\log_{2}(x+4) + \log_{2}(x-2) = 4$

Question 6

If $f(x) = \log_5(x-2)$ , find the value of $f^{-1}(2)$ .

Question 7

Solve the logarithmic equation for $x$ :

\log_3 x + \log_3(x-2) = 1

Question 8

Solve the exponential equation for $x$ by writing both sides with the same base:

4^{x+1} = 8^{x-1}

Question 9

Which of the following expressions is equivalent to $\log_2 7$ using the change of base formula?

Question 10

Solve the exponential equation for $x$ :

9^{x-1} = \left(\dfrac{1}{27}\right)^{x+2}

Logarithmic equations Questionbank