You are Here: Home >< Maths

# Logarithms watch

1. Hello,

Could someone please help me with this problem step by step - not sure how tou get to the answer - can only get so far and :-(

11a) Show that log[4]3 = log[2]sqrt3

11b) Hence or otherwise solve the simultaneous equation:

2log[2]y = log[4]3 + log[2]x

3^y = 9^x

Thanks for you help!
2. (Original post by christinajane)
Hello,

Could someone please help me with this problem step by step - not sure how tou get to the answer - can only get so far and :-(

11a) Show that log[4]3 = log[2]sqrt3

11b) Hence or otherwise solve the simultaneous equation:

2log[2]y = log[4]3 + log[2]x

3^y = 9^x

Thanks for you help!
How did you get on with 11a?
3. (Original post by SeanFM)
How did you get on with 11a?
I got, which I don't even know if its right :

log[4]3 = 1/2log[2]3 = log[2]3^1/2 = log[2]sqrt3

Which seems too obvious????
4. (Original post by christinajane)
I got, which I don't even know if its right :

log[4]3 = 1/2log[2]3 = log[2]3^1/2 = log[2]sqrt3

Which seems too obvious????
It's correct! Keep going.
5. too late ...
6. Oops forgot first line - log[4]3 = log[2]3/log[2]4 = log[2]3/2

but dont really now why that eqals log[2]sqrt3??
7. (Original post by christinajane)
I got, which I don't even know if its right :

log[4]3 = 1/2log[2]3 = log[2]3^1/2 = log[2]sqrt3

Which seems too obvious????
There is a rule you can use to change the base of a logarithm.
loga(b)=[logc(b)]/[logc(a)].
8. Second part I get -

2log[2]y = log[4]3 + log[2}x 3^y = 9^x
y = 2^x (2)
log[2]y^2 = log[2]sqrt3 + log[2]x

y^2 = x(sqrt3) (1)

It follows that:

substituting equation 2 into 1

(2^x)^2 = xsprt3

4x^2 = xsqrt3

then I get stuck...

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 10, 2016
Today on TSR

### University open days

Wed, 25 Jul '18
2. University of Buckingham
Wed, 25 Jul '18
3. Bournemouth University
Wed, 1 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams