IB Middle Years Programme (MYP) · Mathematics

Fractional Exponents, Logarithms and Number Bases (Extended): Practice Questions

3 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Fractional Exponents, Logarithms and Number Bases (Extended).

8 questions20 marksFree, no account

Question 1

1 mark

Solve the equation \(\log_4(2x - 4) = 2\) for \(x\).

Question 2

1 mark

Given that \(\log_b 2 = a\) and \(\log_b 3 = c\), express \(\log_b 18\) in terms of \(a\) and \(c\).

Question 3

1 mark

Find the sum of all real values of \(x\) that satisfy the following equation:
\(\log_2 x + \log_x 16 = 5\)

Question 4

2 marks

Solve for \(x\) in the logarithmic equation: \(\log_3(x + 1) = 2\).

Write your answer out first, then check it against the worked solution.

Question 5

4 marks

Solve for \(x\) in the exponential equation: \(9^{x+1} = 27^{x-1}\).

Write your answer out first, then check it against the worked solution.

Question 6

5 marks

Find all real solutions for \(x\) in the equation: \(4^x - 5(2^x) + 4 = 0\).

Write your answer out first, then check it against the worked solution.

Question 7

2 marks

Solve the following exponential equation for \(x\):
\(3^{x+1} = 81\)

Write your answer out first, then check it against the worked solution.

Question 8

4 marks

Solve the following exponential equation for \(x\):
\(5^{2x} - 6(5^x) + 5 = 0\)

Write your answer out first, then check it against the worked solution.

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