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1EDEXCEL C2 January 2013 Q6
Given that 2log_2(x + 15) - log_2(x) = 6, (a) Show that x^2 - 34x + 225 = 0. (5) (b) Hence, or otherwise, solve the equation 2log_2(x + 15) - log_2(x) = 6. (2)
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2OCR C2 January 2013 Q8
The diagram shows the curves y = log_2(x) and y = log_2(x - 3). (i) Describe the geometrical transformation that transforms the curve y = log_2(x) to the curve y = log_2(x - 3). [2] (ii) The curve y = log_2(x) passes through the point (a, 3). State the value of a. [1] (iii) The curve y = log_2(x - 3) passes through the point (b, 1.8). Find the value of b, giving your answer correct to 3 significant figures. [2] (iv) The point P lies on y = log_2(x) and has an x-coordinate of c. The point Q lies on y = log_2(x - 3) and also has an x-coordinate of c. Given that the distance PQ is 4 units find the exact value of c. [4]
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3EDEXCEL C2 June 2012 Q2
Find the values of x such that 2log_3(x) - log_3(x - 2) = 2. (5)
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4EDEXCEL C2 January 2012 Q4
Given that y = 3x^2, (a) show that log_3(y) = 1 + 2log_3(x). (3) (b) Hence, or otherwise, solve the equation 1 + 2log_3(x) = log_3(28x - 9). (3)
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5EDEXCEL C2 June 2011 Q3
Find, giving your answer to 3 significant figures where appropriate, the value of x for which (a) 5^x = 10, (2) (b) log_3(x - 2) = -1. (2)
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6EDEXCEL C2 January 2011 Q8
(a) Sketch the graph of y = 7^x, x real, showing the coordinates of any points at which the graph crosses the axes. (2) (b) Solve the equation 7^(2x) - 4(7^x) + 3 = 0, giving your answers to 2 decimal places where appropriate. (6)
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Part (a):
7EDEXCEL C2 January 2010 Q5
(a) Find the positive value of x such that log_x(64) = 2. (2) (b) Solve for x: log_2(11 - 6x) = 2log_2(x - 1) + 3. (6)
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Part (b):
8EDEXCEL C2 June 2009 Q8
(a) Find the value of y such that log_2(y) = -3. (2) (b) Find the values of x such that (log_2(32) + log_2(16))/log_2(x) = log_2(x). (5)
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Part (b):
9EDEXCEL C2 January 2009 Q4
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
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10EDEXCEL C2 June 2008 Q4
(a) Find, to 3 significant figures, the value of x for which 5^x = 7. (2) (b) Solve the equation 5^(2x) - 12(5^x) + 35 = 0. (4)
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Part (b):
11EDEXCEL C2 January 2008 Q5
Given that a and b are positive constants, solve the simultaneous equations a = 3b, log_3(a) + log_3(b) = 2. Give your answers as exact numbers. (6)
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Part (a):
12EDEXCEL C2 June 2007 Q6
(a) Find, to 3 significant figures, the value of x for which 8^x = 0.8. (2) (b) Solve the equation 2log_3(x) - log_3(7x) = 1. (4)
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Part (b):
13EDEXCEL C2 January 2007 Q4
Solve the equation 5^x = 17, giving your answer to 3 significant figures. (3)
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14Edexcel A Level June 2022 Paper 2 Q2
(a) Sketch the curve with equation y = 4^x, stating any points of intersection with the coordinate axes. (2) (b) Solve 4^x = 100, giving your answer to 2 decimal places. (2)
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15Edexcel A Level June 2019 Paper 2 Q9
A research engineer is testing the effectiveness of the braking system of a car when it is driven in wet conditions. The engineer measures and records the braking distance, d metres, when the brakes are applied from a speed of V km/h. Graphs of d against V and log_10(d) against log_10(V) were plotted. The results are shown below together with a data point from each graph: (30, 20) on the d against V graph, and (0, -1.77) on the log_10(d) against log_10(V) graph. (a) Explain how Figure 6 would lead the engineer to believe that the braking distance should be modelled by the formula d = kV^n where k and n are constants, with k approximately 0.017. (3) Using the information given in Figure 5, with k = 0.017, (b) find a complete equation for the model giving the value of n to 3 significant figures. (3) Sean is driving this car at 60 km/h in wet conditions when he notices a large puddle in the road 100 m ahead. It takes him 0.8 seconds to react before applying the brakes. (c) Use your formula to find out if Sean will be able to stop before reaching the puddle. (3)
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16Edexcel A Level June 2023 Paper 1 Q6
a = log_2(x), b = log_2(x + 8). Express in terms of a and/or b: (a) log_2(sqrt(x)) (1) (b) log_2(x^2 + 8x) (2) (c) log_2(8 + 64/x). Give your answer in simplest form. (3)
17Edexcel A Level June 2023 Paper 2 Q3
Given that log_2(x + 3) + log_2(x + 10) = 2 + 2log_2(x), (a) show that 3x^2 - 13x - 30 = 0. (3) (b) (i) Write down the roots of the equation 3x^2 - 13x - 30 = 0. (ii) Hence state which of the roots in part (b)(i) is not a solution of log_2(x + 3) + log_2(x + 10) = 2 + 2log_2(x), giving a reason for your answer. (2)
18Edexcel AS June 2023 Paper 1 Q9
Using the laws of logarithms, solve the equation 2log_5(3x - 2) - log_5(x) = 2. (5)
19Edexcel A Level June 2024 Paper 2 Q13
The world human population, P billions, is modelled by the equation P = ab^t, where a and b are constants and t is the number of years after 2004. Using the estimated population figures for the years from 2004 to 2007, a graph is plotted of log_10(P) against t. The points lie approximately on a straight line with gradient 0.0054 and intercept 0.81 on the log_10(P) axis. (a) Estimate, to 3 decimal places, the value of a and the value of b. (4) In the context of the model, (b) (i) interpret the value of the constant a, (ii) interpret the value of the constant b. (2) (c) Use the model to estimate the world human population in 2030. (2) (d) Comment on the reliability of the answer to part (c). (1)
