Question 1
1 markFind the exact solutions to the equation \( 5^{2x} - 12(5^x) + 35 = 0 \).
Pearson Edexcel International A Level · Mathematics (YMA01)
Exponentials and logarithms: Practice Questions
2 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Exponentials and logarithms.
7 questions16 marksFree, no account
Question 2
1 markSolve the equation \( \log_2 x + \log_4 x = 6 \) for \( x \).
Question 3
2 marksSolve the equation \(\log_2(x) = 5\) for \(x\).
Write your answer out first, then check it against the worked solution.
Question 4
3 marksSolve the equation \( 3^{2x-1} = 10 \), giving your answer for \( x \) to 3 decimal places.
Write your answer out first, then check it against the worked solution.
Question 5
2 marksUsing the laws of logarithms, simplify the expression \(\log_a(2x^3) + \log_a(\frac{1}{x})\) into a single logarithm in its simplest form.
Write your answer out first, then check it against the worked solution.
Question 6
3 marksUsing the laws of logarithms, solve the following equations:
(a) \(\log_{2}(x+3) + \log_{2}(x-3) = 4\), giving your answer as a simplified surd if necessary.
(b) \(2\log_{3}(y+1) - \log_{3}(2y-1) = 1\).
Write your answer out first, then check it against the worked solution.
Question 7
4 marksSolve the equation \(3^{2x} - 10(3^x) + 9 = 0\).
Write your answer out first, then check it against the worked solution.
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