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Help! A2 Maths logarithms are so confusing!
Hi, there are some of these examination-type questions which I can't do. I know I should do it myself but I have tried reading the chapter over and over again. I'm using the 'Heinemann Modular Mathematics for Edexcel AS and A2 Level' P2 book, which is green but it's so crap! It gives you examples but only to do the easy ones such as 'Solve 3(4^2x) + 11(4^x) = 4' by using logarithms. I'm not bothered about the answer since the answers are basically at the back of the book. What I'm more interested in is how you do them so that if a similar question was to appear later in an exam or something, I would be able to answer it. This book doesn't explain anything and just gives the laws of logaritms and some simple examples to explain them.
Anyways, if anyone is willing to help, here are the 5 questions which I'm stuck on (which can be found on pg113 if you have the book ready):
Note: I shall be using . as the beginning and end of a number in lower case because I dunno how to type it although I know that ^ is to the power of.
- Find the values of x for which log.3.x - 2log.x.3 = 1
- Solve the equation log.3.(2-3x) = log.9.(6x^2 - 19x + 2)
- Find the possible values of x for which 2^(2x+1) = 3(2^x) - 1
- If xy = 64 and log.x.y + log.y.x = 5/2, find x and y
- Prove that if a^x = b^y = (ab)^(xy), then x + y = 1
Sorry if the questions look confusing but I couldn't do the underscore for what is known as the base so I had to open and close it with a full stop.
I'm not desperate but I would really appreciate if someone could explain to me how to do these because I have no idea and the book is useless. Thanks.
Anyways, if anyone is willing to help, here are the 5 questions which I'm stuck on (which can be found on pg113 if you have the book ready):
Note: I shall be using . as the beginning and end of a number in lower case because I dunno how to type it although I know that ^ is to the power of.
- Find the values of x for which log.3.x - 2log.x.3 = 1
- Solve the equation log.3.(2-3x) = log.9.(6x^2 - 19x + 2)
- Find the possible values of x for which 2^(2x+1) = 3(2^x) - 1
- If xy = 64 and log.x.y + log.y.x = 5/2, find x and y
- Prove that if a^x = b^y = (ab)^(xy), then x + y = 1
Sorry if the questions look confusing but I couldn't do the underscore for what is known as the base so I had to open and close it with a full stop.
I'm not desperate but I would really appreciate if someone could explain to me how to do these because I have no idea and the book is useless. Thanks.
jediknight007
Hi, there are some of these examination-type questions which I can't do. I know I should do it myself but I have tried reading the chapter over and over again. I'm using the 'Heinemann Modular Mathematics for Edexcel AS and A2 Level' P2 book, which is green but it's so crap! It gives you examples but only to do the easy ones such as 'Solve 3(4^2x) + 11(4^x) = 4' by using logarithms. I'm not bothered about the answer since the answers are basically at the back of the book. What I'm more interested in is how you do them so that if a similar question was to appear later in an exam or something, I would be able to answer it. This book doesn't explain anything and just gives the laws of logaritms and some simple examples to explain them.
Anyways, if anyone is willing to help, here are the 5 questions which I'm stuck on (which can be found on pg113 if you have the book ready):
Note: I shall be using . as the beginning and end of a number in lower case because I dunno how to type it although I know that ^ is to the power of.
- Find the values of x for which log.3.x - 2log.x.3 = 1
- Solve the equation log.3.(2-3x) = log.9.(6x^2 - 19x + 2)
- Find the possible values of x for which 2^(2x+1) = 3(2^x) - 1
- If xy = 64 and log.x.y + log.y.x = 5/2, find x and y
- Prove that if a^x = b^y = (ab)^(xy), then x + y = 1
Sorry if the questions look confusing but I couldn't do the underscore for what is known as the base so I had to open and close it with a full stop.
I'm not desperate but I would really appreciate if someone could explain to me how to do these because I have no idea and the book is useless. Thanks.
Anyways, if anyone is willing to help, here are the 5 questions which I'm stuck on (which can be found on pg113 if you have the book ready):
Note: I shall be using . as the beginning and end of a number in lower case because I dunno how to type it although I know that ^ is to the power of.
- Find the values of x for which log.3.x - 2log.x.3 = 1
- Solve the equation log.3.(2-3x) = log.9.(6x^2 - 19x + 2)
- Find the possible values of x for which 2^(2x+1) = 3(2^x) - 1
- If xy = 64 and log.x.y + log.y.x = 5/2, find x and y
- Prove that if a^x = b^y = (ab)^(xy), then x + y = 1
Sorry if the questions look confusing but I couldn't do the underscore for what is known as the base so I had to open and close it with a full stop.
I'm not desperate but I would really appreciate if someone could explain to me how to do these because I have no idea and the book is useless. Thanks.
Hi, I use the notation log_a(b) for the log of b to the base a.
> log.3.x - 2log.x.3 = 1
log_3(x) - 2log_x(3) = 1
log_3(x) - 2log_3(3)/log_3(x) = 1
(log_3(x))^2 - 2 = log_3(x)
(log_3(x))^2 - log_3(x) - 2 = 0
That's a quadratic equation. Let y = log_3(x), so:
y^2 - y - 2 = 0
(y - 2)(y + 1) = 0
Therefore y = 2 or y = -1
So, log_3(x) = 2 or log_3(x) = -1
So, x = 3^2 or 3^(-1)
= 9 or 1/3> log.3.(2-3x) = log.9.(6x^2 - 19x + 2)
log_3(2 - 3x) = log_9(6x^2 - 19x + 2)
9^(log_3(2 - 3x)) = 6x^2 - 19x + 2
(3^(log_3(2 - 3x)))^2 = 6x^2 - 19x + 2
(2 - 3x)^2 = 6x^2 - 19x + 2
9x^2 - 12x + 4 = 6x^2 - 19x + 2
3x^2 + 7x + 2 = 0
(3x + 1)(x + 2) = 0
So x = -1/3 or x = -2> 2^(2x+1) = 3(2^x) - 1
Let y = 2^x, so:
2y^2 = 3y - 1
(2y - 1)(y - 1) = 0
Therefore y = 1/2 or y = 1
So x = log_2(1/2) or x = log_2(1)
So x = -1 or x = 0> If xy = 64 and log.x.y + log.y.x = 5/2, find x and y
log_x(y) + log_y(x) = 5/2
Using change of base rule:
log_x(y) + log_x(x)/log_x(y) = 5/2
(log_x(y))^2 + 1 = 5/2log_x(y)
That's a quadratic equation. Let z = log_x(y), so:
z^2 - (5/2)z + 1 = 0
(z - 5/4)^2 - 9/16 = 0
z = +/-3/4 + 5/4
So z = 2 or z = 1/2
So, log_x(y) = 2 or log_x(y) = 1/2
We have xy = 64, so y = 64/x:
So, log_x(64/x) = 2 or log_x(64/x) = 1/2
So, log_x(64) - log_x(x) = 2 or log_x(64) - log_x(x) = 1/2
So, log_x(64) = 3 or log_x(64) = 3/2
So, ln(64)/ln(x) = 3 or ln(64)/ln(x) = 3/2
So, ln(x) = ln(64)/3 or ln(x) = (2/3)ln(64)
So, x = 4 or x = 16
xy = 64, so when x = 4, y = 64/4 = 16 and when x = 16, y = 64/16 = 4We have then two solution sets, (4, 16) and (16, 4). We should expect that they are the reverse of each other, as in the question you could swap x for y without changing the meaning of the question.
> Prove that if a^x = b^y = (ab)^(xy), then x + y = 1
Well from that we have:
a^x = (ab)^(xy)
ln(a^x) = ln((ab)^(xy))
xln(a) = (xy)ln(ab)
y = ln(a)/ln(ab)
We also have:
b^y = (ab)^(xy)
ln(b^y) = ln((ab)^(xy))
yln(b) = (xy)ln(ab)
x = ln(b)/ln(ab)
Therefore:
x + y = ln(b)/ln(ab) + ln(a)/ln(ab) = (ln(a) + ln(b))/ln(ab) = ln(ab)/ln(ab) = 1
Q.E.D.I hope this helps you.
Regards,
Wow! Thanks a lot, that really helped. From now on, I shall be using your way of giving underscore numbers. Thanks!
rahaydenuk
No problem 
ahhhhhhhhhhhhhhhh, ive just realised someithng. im going to do a maths degree a week on monday...i dont even know what all that up there means.
aghhhhhhhhhhhhhhhhhhhh
love Katy ***
ickle_katy
ahhhhhhhhhhhhhhhh, ive just realised someithng. im going to do a maths degree a week on monday...i dont even know what all that up there means.
aghhhhhhhhhhhhhhhhhhhh
love Katy ***
aghhhhhhhhhhhhhhhhhhhh
love Katy ***
Maybe you should do a quick bit of revision before you go, just to refresh your mind before you get there?
You could read over A-level notes etc., just to get back into a mathematical state of mind.I started on Trigonometry today and although it has been easy so far, it's bloody 30 pages long! I think this is one of the hardest topics ever. The original trigonometry in AS was ok, where you just find the values of x etc... but this topic introduces secants, cosecants and cotangents and there are like 15 different formulas to remember! 100% definite interference for my LTM then! Had the logarithms test today as well and I think I only got half of the questions right.
If ln is a natural log, are the others artificial ones?
Surfing Hamster
If ln is a natural log, are the others artificial ones?
e is called the "natural" nuber because the derivative/integral of e^x is itself (the only function which this is true). A logarithm to the base e is therefore given the name "natural logarithm", however, the other logarithms are not artificial, just natural in their own special way.
(you can tell im becoming a counsellor for the "special" logarithms)
elpaw
e is called the "natural" nuber because the derivative/integral of e^x is itself (the only function which this is true). A logarithm to the base e is therefore given the name "natural logarithm", however, the other logarithms are not artificial, just natural in their own special way.
(you can tell im becoming a counsellor for the "special" logarithms)
(you can tell im becoming a counsellor for the "special" logarithms)
*falls over*
and and and jon loves rushda!!!!
jediknight007
I'm using the 'Heinemann Modular Mathematics for Edexcel AS and A2 Level' P2 book, which is green but it's so crap!
I hated those books too. Completely useless. The worst thing is spending 1 hr+ struggling with a single question only to get to school and find the answer in the back of the book is wrong...
I think the textbook was actually the worst thing about Maths A level, now that I think of it.
++Hex++
I hated those books too. Completely useless. The worst thing is spending 1 hr+ struggling with a single question only to get to school and find the answer in the back of the book is wrong...
I think the textbook was actually the worst thing about Maths A level, now that I think of it.
I think the textbook was actually the worst thing about Maths A level, now that I think of it.
I have been using these Edexcel books ever since Year 10 and they have quite a lot of silly mistakes in their answers at the back of the book, even the piss-easy ones. And it's kinda useless giving you the answer and not telling you how to do it as well. I wouldn't mind that if the examples in the book were better! They give you examples like y=sinx for example but some of the questions are ridiculously difficult. It's a good thing my teacher is always willing to help out.
jediknight007
I have been using these Edexcel books ever since Year 10 and they have quite a lot of silly mistakes in their answers at the back of the book, even the piss-easy ones. And it's kinda useless giving you the answer and not telling you how to do it as well. I wouldn't mind that if the examples in the book were better! They give you examples like y=sinx for example but some of the questions are ridiculously difficult. It's a good thing my teacher is always willing to help out.
They never go over the answers to 'show that.../prove...' questions, which is a bit miserly, but they explain the concepts well (except for the bit on half-angle formulae in P2 - that bit really IS crap) and have loads of questions on each topic.
Ben
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- What A-level maths skills are required in A-level chemistry and biology?
- a level maths study materials
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