# C2 Exponentials and Logarithms Help

1) Given that a = log(10)2 and b = log(10)3, find the expressions in terms of a and b for [(10) meaning a small 10]

a) log(10)1.5
b) log(10)24
c) log(10)150

Ive worked out a) which is b/a and Ive worked out b) aÂ³b (not entirely sure if thats right) but I'm having trouble with trying to find the figures for c)
factorise 150 into prime factors? I'm not sure it'll work, but it is worth a try...

edit: won't work work me... hence a bad idea probably
lilydelarocks
1) Given that a = log(10)2 and b = log(10)3, find the expressions in terms of a and b for [(10) meaning a small 10]

a) log(10)1.5

Here
OH yes I forgot bout that..I've just taught myself this topic as I was never taught this by a teacher so Im more likely to make mistakes with this topic...

Unfortunately for me, I've been set homework to do a whole sheet on Exponentials and Logarithms..
Question: does that mean b) is 3a + b..?

Explanation:
log(10)24
= log(10)2Â³ x log(10)3
= 3log(10)2 x log(10)3
= 3a + b

EDIT: ok I see I am correct..YIPEEEE
lilydelarocks
OH yes I forgot bout that..I've just taught myself this topic as I was never taught this by a teacher so Im more likely to make mistakes with this topic...

Unfortunately for me, I've been set homework to do a whole sheet on Exponentials and Logarithms..

I think you should have been given log(10) 5
steve2005
I think you should have been given log(10) 5

I agree, I was scratching my head for trying to figure that one out with multiples of 2 and 3, which I coudn't...
OK thanks guys..

But Im stuck on another question:
4log(3)x - 5 = 0

I have:
4log(3)x - log(10)10^5 = 0

But not sure what to do next...Im stuck with bringing the
log(10)10^5 over to the other side and doing something else but then again, Im not sure what I would do next if i do that..
lilydelarocks
OK thanks guys..

But Im stuck on another question:
4log(3)x - 5 = 0
..

If you want x then the answer is 3.948(3 d.p)
OK Thanks

Sorry to bother you guys again on this topic..
but i have another question:

log(3)xÂ³ - 5log(3)x = 4

Is this right?
log(3)xÂ³/5log(3)x = 4
1/5xÂ² = 4
xÂ² = 20
x = 4.472135955
lilydelarocks
OK Thanks

Sorry to bother you guys again on this topic..
but i have another question:

log(3)xÂ³ - 5log(3)x = 4

Is this right?
log(3)xÂ³/5log(3)x = 4
1/5xÂ² = 4
xÂ² = 20
x = 4.472135955

Many calculators can work out logs in different bases. e.g casio fx 83ES So you can check your answers.
steve2005
I think you should have been given log(10) 5

log(10) 5 = 1 - log(10) 2

lilydelarocks: You should be able to use this to work out the c) part of your first question.
ukgea
log(10) 5 = 1 - log(10) 2

Clever. Using your hint I have done it slightly different.
Oh ok thanks..man I'm going to really struggle with this worksheet and this whole topic in general ...
lilydelarocks
Oh ok thanks..man I'm going to really struggle with this worksheet and this whole topic in general ...

Do you know about MathsNet ?

http://www.mathsnet.net/asa2/2004/c25loglaws_1.html
I don't even have an idea of how to work out this question:

An initial investment of Â£1000 is places into a savings account that offers 2.2% interest every 3 months. The amount of money in the account Â£P, at the end of t years is fiven by

P = 1000 X 1.022 ^(4t) ....( and that's a mutiply sign btw)

Find, to the nearest year, how long it will take for the investment to double in value. (4 marks)
i.e. you have to solve $2000=1000\times1.022^{4t}$

edit: t must be rounded up to nearest integer if I'm not missing anything
lilydelarocks
I don't even have an idea of how to work out this question:

An initial investment of Â£1000 is places into a savings account that offers 2.2% interest every 3 months. The amount of money in the account Â£P, at the end of t years is fiven by

P = 1000 X 1.022 ^(4t) ....( and that's a mutiply sign btw)

Find, to the nearest year, how long it will take for the investment to double in value. (4 marks)

This is a hint, while I figure out what is needed....
lilydelarocks
.

I guess I have been beaten.

Edit: You can use ln or log base 10 or any other logarithm base. Most calculators can work out natural logs and logs to base 10.