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1EDEXCEL C3 June 2014 Q2
Find the exact solutions, in their simplest form, to the equations (a) 2ln(2x + 1) - 10 = 0 (2) (b) 3^x e^(4x) = e^7 (4)
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Part (a):
Part (b):
2EDEXCEL C3 June 2013 Q2
Given that f(x) = ln(x), x > 0, sketch on separate axes the graphs of (i) y = f(x), (ii) y = |f(x)|, (iii) y = -f(x - 4). Show, on each diagram, the point where the graph meets or crosses the x-axis. In each case, state the equation of the asymptote. (7)
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Part (a):
3EDEXCEL C3 June 2013 Q6
Find algebraically the exact solutions to the equations (a) ln(4 - 2x) + ln(9 - 3x) = 2ln(x + 1), -1 < x < 2 (5) (b) 2^x e^(3x+1) = 10. Give your answer to (b) in the form (a + ln(b))/(c + ln(d)) where a, b, c and d are integers. (5)
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Part (b):
4OCR C3 June 2012 Q2
It is given that p = e^280 and q = e^300. (i) Use logarithm properties to show that ln(ep^2/q) = 261. [3] (ii) Find the smallest integer n which satisfies the inequality 5^n > pq. [3]
