Questions and Answers of Financial Accounting Information For Decisions

Solve.a. log2 x + log2 4 = log2 20b. log4 2x – log4 5 = log4 3c. log4 (x – 5) + log4 5 = 2 log4 10d. log3 (x + 3) = 2 log3 4 + log3 5
Solve, giving your answers correct to 3 sf.a. 2x = 70b. 3x = 20c. 5x = 4d. 23x = 150e. 3x+1 = 55f. 22x+1 = 20g. 7x-5 = 40h. 7x = 3x+4i. 5x+1 = 3x+2j. 4x-1 = 5x+1k. 32x+3 = 53x+1l. 34-5x = 2x+4
Given that u = log4x, find, in simplest form in terms of u.a. logx 4,b. logx 16,c. logx 2.d. logx 8.
Use a calculator to evaluate correct to 3 sf.a. ln 4b. ln 2.1c. ln 0.7d. ln 0.39
Solve each of these equations, giving your answers correct to 3 sf.a. 10x = 75b. 10x = 300c. 10x = 720d. 10x = 15.6e. 10x = 0.02f. 10x = 0.005
Convert from logarithmic form to exponential form.a. log2 4 = 2b. log2 64 = 6c. log5 1 = 0d. log3 9 = 2e. log36 6 = ½f. log8 2 = 1/3g. logx 1 = 0h. logx 8 = yi. loga b = c
At the beginning of 2015, the population of a species of animals was estimated at 50,000. This number decreased so that, after a period of n years, the population was 50,000e-0.03n.a. Estimate the
Use a graphing software package to plot each of the following family of curves for k = 3, 2, 1, - 1, - 2 and – 3.a. y = ln kxb. y = k ln xc. y = ln(x + k)Describe the properties of each family of
Sketch the graphs of each of the following logarithmic functions. [ Remember to show the axis crossing points and the asymptotes.]a. y = ln(2x + 4)b. y = ln (3x – 6)c. y = ln (8 – 2x)d. y =
Find f-1(x) for each function.a. f(X) = ln(x + 1), x > - 1b. f(x) = ln(x – 3), x > 3c. f(x) = 2ln(x + 2), x > - 2d. f(x) = 2ln(2x + 1), x > - ½e. f(x) = 3ln (2x – 5), x > 5/2f.
Solve the following simultaneous equations.Log2(x + 3) = 2 + log2 yLog2(x + y) = 3
Write as a single logarithm, then simplify your answer.a. log2 56 – log2 7b. log6 12 + log6 3c. ½ log2 36 – log2 3d. log3 15 – ½ log3 25e. log4 40 – 1/3 log4 125f. ½ log3 16 – 2 log3 6
Solve.a. log6 x + log6 3 = 2b. lg(5x) – lg(x – 4) = 1c. log2(x + 4) = 1 + log2(x – 3)d. log3(2x + 3) = 2 + log3(2x – 5)e. log5(10x + 3) – log5 (2x – 1) = 2f. lg(4x + 5) + 2lg2 = 1 + lg(2x
a. Show that 2x+1 – 2x-1 = 15 can be written as 2(2x) – ½(2x) = 15.b. Hence find the value of 2x.c. Find the value of x.
Given that log9 y = x, express in terms of x.a. logy 9,b. log9 (9y)c. log3y,d. log3(81y).
Without using a calculator find the value ofa. eln 5b. e1/2 ln64c. 3eln2d. -e-ln1/2
Convert from logarithmic form to exponential form.a. lg 1000000 = 5b. lg 10 = 1c. lg 1/1000 = - 3d. lg x = 7/5e. lg x = 1.7f. lg x = - 0.8
Solve.a. log2 x = 4b. log3 x = 2c. log5 x = 4d. log3 x = ½e. logx 144 = 2f. logx 27 = 3g. log2 (x – 1) = 4h. log3 (2x + 1) = 2i. log5 (2 – 3x) = 3
The volume of water in a container, V cm3, at time t minutes, is given by the formulaV = 2000 e-kt.When V = 1000, t = 15.a. Find the value of k.b. Find the value of V when t = 22.
F(x) = e2x + 1 for x ∈ Ra. State the ranger of f(x).b. Find f-1(x)c. State the domain of f-1(x).d. Find f-1f(x)
Functions g and h are defined byg(x) = 4ex – 2 for x ∈ R,h(x) = ln 5x for x > 0.a. Find g-1(x).b. Solve gh(x) = 18.
Simplifya.b. 2log,3 - log, 4 + log,8
Solve.a. log5 (x + 8) + log5 (x + 2) = log5 20xb. log3 x + log3 (x – 2) = log3 15c. 2 log4 x – log4 (x + 3) = 1d. lg x + lg(x + 1) = lg 20e. log3 x + log3(2x – 5) = 1f. 3 + 2 log2 x = log2 (14x
Solve, giving your answers correct to 3 sf.a. 2x+2 – 2x = 4b. 2x+1 – 2x-1 – 8 = 0c. 3x+1 – 8(3x-1) – 5 = 0d. 2x+2 – 2x-3 = 12e. 5x – 5x+2 + 125 = 0
a. Given that logp x = 20 and logp y = 5, find logy x.b. Given that logp X = 15 and logp Y = 6, find the value of logx Y.
Solve.a. eln x = 7b. ln ex = 2.5c. eln x = 36d. e-ln x = 20
Solve each of these equations, giving your answers correct to 3 sf.a. lg x = 5.1b. lg x = 3.16c. lg x = 2.16d. lg x = - 0.3e. lg x = - 1.5f. lg x = - 2.84
Solve.a. logx 64 – logx 4 = 1b. logx 16 + logx 4 = 3c. logx 4 – 2logx 3 = 2d. logx 15 = 2 + logx 5
Without using a calculator, find the value ofa. lg 10,000b. lg 0.01c. lg √10d. lg (3√10)e. lg (10√10)f. lg (1000/√10).
Find the value ofa. log4 16b. log3 81c. log4 64d. log2 0.25e. log3 243f. log2 (8√2)g. log5 (25√5)h. log2 (1/√8)i. log64 8j. log7 (√7/7)k. log5 3√5l. log3 1/√3
A species of fish is introduced to a lake.The population, N, of this species of fish after t weeks is given by the formulaN = 500 e-0.3t.a. Find the initial population of these fish.b. Estimate the
F(x) = ex for x ∈ R. g(x) = ln 5x for x > 0a. Findi. fg(x)ii. gf(x).b. Solve g(x) = 3f-1(x).
Given that logP X = 5 and logP Y = 2y finda. logP X2,b. logP 1/X,c. logXY P.
a. Express 16 and 0.25 as powers of 2.b. Hence, simplify log3 16/log3 0.25.
Use the substitution y = 3x to solve the equation 32x + 2 = 5(3x).
Evaluate logp 2 × log8p.
Solve, giving your answers correct to 3 sf.a. ex = 70b. e2x = 28c. ex+1 = 16d. e2x-1 = 5
Simplify.a. logx x2b. logx 3√xc. logx (x√x)d. logx 1/x2e. logx (1/x2)3f. logx (√x7)g. logx (x/3√x)h. logx (x√x/3√x)
The value, $V, of a house n years after it was built is given by the formulaV = 250,000 ean.When n = 3, V = 350,000.a. Find the initial value of this house.b. Find the value of a.c. Estimate the
F(x) = e3x for x ∈ R. g(x) = ln x for x > 0a. Findi. fg(x)ii. gf(x).b. Solve f(x) = 2g-1(x).
Solve.a. log9 3 + log9(x + 4) = log5 25b. 2 log4 2 + log7(2x + 3) = log3 27
a. Given that log4 x = 1/2, find the value of x.b. Solve 2 log4 y – log4(5y – 12) = ½,
Simplify.a. log7 4 / log7 2b. log7 27 / log7 3c. log3 64 / log3 0.25d. log5 100 / log5 0.01
Solve.a. (log5 x2) – 3log5(x) + 2 = 0b. (log5 x)2 – log5(x2) = 15c. (log5 x)2 – log5(x3) = 18d. 2(log2 x)2 + 5log2 (x2) = 72
Solve, giving your answer correct to 3 sf. za. 32x – 6 × 3x + 5 = 0b. 42x – 6 × 4x – 7 = 0c. 22x – 2x – 20 = 0d. 52x – 2(5x) – 3 = 0
Use the substitution u = 5x to solve the equation 52x – 2(5x+1) + 21 = 0.
Solve, giving your answers in terms of natural logarithms.a. ex = 7b. 2ex + 1 = 7c. e2x-5 = 3d. 1/2 e3x-1 = 4
Solve.a. log3 (log2 x) = 1b. log2 (log5 x) = 2
F(x) = e2x for x ∈ R. g(x) = ln(2x + 1) for x > - ½a. Find fg(x).b. Solve f(x) = 8g-1(x).
The area, A cm2, of a patch of mould is measured daily.The area, n days after the measurements started, is given by the formulaA = A0bn.When n = 2, A = 1.8 and when n = 3, A = 2.4.a. Find the value
Solve the equation 32x = 1000, giving your answer to 2 decimal places.
Given that u = log5 x, find, in simplest form in terms of u.a. xb. log5 (x/25)c. log5 (5√x)d. log5 (x√x / 125).
Solve the simultaneous equations.a. xy = 64logx y = 2b. 2x = 4y2lg y = lg x + lg 5c. log4(x + y) = 2 log4 xlog4 y = log4 3 + log4 xd. xy = 6402 log10 x – log10 y = 2e. log10 a = 2 log10 blog10
Solve, giving your answers correct to 3 sf.a. 22x + 2x+1 – 15 = 0b. 62x – 6x+1 + 7 = 0c. 32x – 2(3x+1) + 8 = 0d. 42x+1 = 17 (4x) - 15
a. Express log4 x in terms of log2 x.b. Using your answer of part a, and the substitution u = log2 x, solve the equation log4 x + log2 x = 12.
Solve, giving your answers correct to 3 sf.a. ln x = 3b. ln x = - 2c. ln (c + 1) = 7d. ln (2x – 5) = 3
Express lg a + 3lg b – 3 as a single logarithm.
Given that log4 p = x and log4 q = y, express in terms of x and/ or ya. log4 (4p)b. log4 (16/p)c. log4p + log4 q2d. pq.
a. Show that lg(x2 y) = 18 can be written as 2 lg x + lg y = 18.b. lg(x2 y) = 18 and lg (x/y3) = 2.Find the value of lg x and lg y.
Solve.a. log2 x + 5 log4 x = 14b. log3 x + 2 log9 x = 4c. 5 log2 x – log4 x = 3d. 4 log3 x = log9 x + 2
Solve, giving your answers correct to 3 sf.a. 4x – 3(2x) – 10 = 0b. 16x + 2(4x) – 25 = 0c. 9x – 2(3x+1) + 8 = 0d. 25x + 20 = 12(5x)
Solve, giving your answers correct to 3 sf.a. ln x3 + ln x = 5b. e3x+4 = 2ex- 1c. ln(x + 5) – ln x = 3
Using the substitution u = 5x, or otherwise, solve52x+1 = 7 (5x) – 2.
Given that loga x = 5 and loga y = 8, finda. loga (1/y)b. loga (√x/y)c. loga (xy)d. loga (x2y3).
a. Express logx 3 in terms of a logarithm to base 3.b. Using your answer of part a, and the substitution u = log3 x, solve the equation log3 x = 3 – 2logx 3.
32x+1 × 5x-1 = 27x × 52xFind the value ofa. 15xb. x.
Solve, giving your answers in exact form.a. ln(x – 3) = 2b. e2x-1 = 7c. e2x – 4ex = 0d. ex = 2e-xe. e2x – 9ex + 20 = 0f. ex + 6e-x = 5
The temperature, T° Celsius, of an object, t minutes after it is removed from a heat source, is given byT = 55 e-0.1t + 15.a. Find the temperature of the object at the instant it is removed from the
Given that loga x = 12 and loga y = 4, find the value ofa. loga (x/y)b. loga (x2/y)c. loga (x√y)d. loga (y/3√x).
Solve.a. log3 x = 9 logx 3b. log5 x + logx 5 = 2c. log4 x – 4 logx 4 + 4 = 0d. log4 x + 6 logx 4 – 5 = 0e. log2 x – 9 logx 2 = 8f. log5 y = 4 – 4 logy 5
Solve the equations, giving your answers correct to 3 significant figures.a. |3x + 2| = |3x – 10|b. |2x+1 + 3| = |2x + 10|c. 32|x| = 5(3|x|) + 24d. 4|x| = 5(2|x|) + 14
Solve, giving your answers correct to 3 sf.a. e2x – 2ex – 24 = 0b. e2x – 5ex + 4 = 0c. ex + 2e-x = 80
a. Write log27 x as a logarithm to base 3.b. Given that loga y = 3(loga 15 – loga 3) + 1, express y in terms of a.
a. Express log4 x in terms of log2 x.b. Express log8 y in terms of log2 y.c. Hence solve, the simultaneous equations6 log4 x + 3 log8 y = 16log2 x – 2 log4 y = 4
Solve the inequality |2x+1 – 1| < 2x – 8| giving your answer in exact form.
Solve the simultaneous equations, giving your answers in exact form.a. ln x = 2 ln yln y – ln x = 1b. e5x-y = 3e3xe2x = 5ex+y
Do not use a calculator in this question.i. Find the value of – logP P2.ii. Find lg(1/10n).iii. Show that lg20-lg4/log5 10 = (lg y)2, where y is a constant to be found.iv. Solve logt 2x + logt 3x =
Solve the simultaneous equations2 log3 y = log5 125 + log3 x2y = 4x.
Solve 5 ln(7 – e2x) = 3, giving your answer correct to 3 significant figures.
a. i. Sketch the graph of y = ex – 5, showing the exact coordinates of any points where the graph meets the coordinate axes.ii. Find the range of values of k for which the equation ex – 5 = k has
Solve ex – xe5x-1 = 0.
a. Solve the following equations to find P and q.8q-1 × 22P+1 = 479P-4 × 3q = 81b. Solve the equation lg(3x – 2) + lg(x + 1) = 2 – lg 2.
Solve 5x2 – x2 e2x + 2e2x = 10 giving your answers in exact form.
Find the real values of x satisfying the following equations.a. x4 – 5x2 + 4 = 0b. x4 + x2 – 6 = 0c. x4 – 20x2 + 64 = 0d. x4 + 2x2 – 8 = 0e. x4 – 4x2 – 21 = 0f. 2x4 – 17x2 – 9 = 0g.
Solve the equation |2x – 3| = |3x – 5|.
Solve.a. |2x – 1| = |x|b. |x + 5| = |x – 4|c. |2x – 3| = |4 – x|d. |5x + 1| = |1 – 3x|e. |1 -4x| = |2 - x|f.g.|3x - 2| = |2x + 5|h. |2x - 1| = 2|3 - x|i. =|3x+2| 2|
The graphs of y = |x – 2| and y = |2x – 10| are shown on the grid.Write down the set of values of x that satisfy the inequality |x – 2|> |2x – 10|. 8- 7- y = Ix -2| 6- 5- 4- y 12x-10| !!
Find the coordinates of the points A, B and C where the curve intercepts the x-axis and the point D where the curve intercepts the positive y-axis. y = (x- 2) (x + 1)(x-3) D A B
The diagram shows part of the graph of y = x(x – 2) (x + 1).Use the graph to solve each of the following inequalities.a. x(x – 2) (x + 1) ≤ 0,b. x(x – 2) (x + 1) ≥ 1,c. x(x – 2) (x + 1)
Use the quadratic formula to solve these equations.Write your answers correct to 3 significant figures.a. x4 – 8x2 + 1 = 0b. x4 – 5x2 – 2 = 0c. 2x4 + x2 – 5 = 0d. 2x6 – 3x3 – 8 = 0e. 3x6
Solve the inequality |2x – 1| > 7.
Solve the simultaneous equations y = |x – 5| and y = |8 – x|.
a. On the same axes sketch the graphs of y = |3x – 6| and y = |4 – x|.b. Solve the inequality |3x – 6| ≥ |4 – x|.
Sketch each of these curves and indicate clearly the axis intercepts.a. y = (x – 2) (x – 4) (x + 3)b. y = (x + 2) (x + 1) (3 – x)c. y = (2x + 1) (x + 2) (x -2)d. y = (3 – 2x) (x – 1) (x + 1)
The diagram shows part of the graph of y = (x + 1)2 (2 - x).Use the graph to solve each of the following inequalities.a. (x + 1)2 (2 - x) ≥ 0,b. (x + 1)2 (2 - x) ≤ 4,c. (x + 1)2 (2 - x) ≤ 3. yt
Solve.a.b.c.d.e. 8x - 18√x + 9 = 0f. 6x + 11√x – 35 = 0g. 2x + 4 = 9√xh.i. x-7Vx+10=0
Solve the inequality |7 – 5x| < 3.
Solve the equation 6|x + 2|2 + 7|x + 2| - 3 = 0.
Solve.a. |2x – 3| > 5b. |4 – 5x| ≤ 9c. |8 – 3x| < 2d. |2x – 7| > 3e. |3x + 1| > 8f. |5 – 2x| ≤ 7
Find the coordinates of the point A and the point B, where A is the point where the curve intercepts the positive x-axis and B is the point where the curve intercepts the positive y-axis. y = 2(x+ 1)

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