Question 1
1 markSimplify the expression \(\frac{\sqrt{18} + \sqrt{32}}{\sqrt{2}}\).
Pearson Edexcel IGCSE · Further Pure Mathematics
Logarithmic functions and indices: Practice Questions
5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Logarithmic functions and indices.
10 questions26 marksFree, no account
Question 2
1 markGiven that \(\log_3 x - 2\log_x 3 = 1\), find the possible values of \(x\).
Question 3
1 markThe equation \(\log_x 6561 + 2 = \log_3 x\) has two real solutions, \(\alpha\) and \(\beta\).
Find the value of the product \(\alpha\beta\).
Question 4
1 markSolve the equation \(8^{x-1} = 16\) for \(x\).
Question 5
1 markGiven that \(\log_{3} (x+2) - \log_{3} x = 2\), find the value of \(x\).
Question 6
3 marksSolve the equation \(\log_5(2x + 7) - \log_5(x - 1) = 1\).
Write your answer out first, then check it against the worked solution.
Question 7
4 marksSolve the equation \( 25^{x-1} = 125^{x+2} \).
Write your answer out first, then check it against the worked solution.
Question 8
5 marksSolve the equation \( \log_3 (x+5) - \log_3 (x-3) = 2 \).
Write your answer out first, then check it against the worked solution.
Question 9
4 marksSolve the equation \( 27^{2x-1} = \frac{1}{9^x} \).
Write your answer out first, then check it against the worked solution.
Question 10
5 marksSolve the equation \( 2 \log_3 x = \log_3 (x+6) \).
Write your answer out first, then check it against the worked solution.
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