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# logs watch

1. ok i think im bein abit thick but i keep gettin the wrong answer

solve the equation 3^2x=4^2-x

thanks!
2. do u mean 4^2 - x or 4^(2-x)?
3. ok i think im bein abit thick but i keep gettin the wrong answer

solve the equation 3^2x=4^2-x

thanks!

2xlog3 = 2-xlog4
2xlog3 - (2-xlog4) = 0
sry im tired i can't think

factorise that by taking x as a common letter you will get x( something something) Thus you can solve for x, i think that's how you do it. I haven't completed my c2 logs bit yet.
4. 2xlog3 = 2-xlog4
2x/2-x = log4/log3

but then thats difficult to find x from there
2xlog3 = 2-xlog4
2x/2-x = log4/log3

but then thats difficult to find x from there
if thats true then
log4/log3 = 1.26...

2x/(2-x) = 1.26...
2x = (2-x)1.26
2x = 2.52...-1.26..x
2x - 1.26x = 2.52
0.73x = 2.52..
x = 2.52/0.73
x = 3.419022...

or
x = 2(log4/log3)/(2 - [log4/log3])
6. (Original post by manps)
if thats true then
log4/log3 = 1.26...

2x/(2-x) = 1.26...
2x = (2-x)1.26
2x = 2.52...-1.26..x
2x - 1.26x = 2.52
0.73x = 2.52..
x = 2.52/0.73
x = 3.419022...

or
x = 2(log4/log3)/(2 - [log4/log3])
???????????????
7. try my method :P
another method..
3^2x=4^2-x

take logs to the base 3 of each side
you will get [logs are to the base 3 here]
2x = (2-x)log4
2x / (2-x) = log 4

or take logs to the base 4
2xlog3 = 2-x
2-x / 2x = log 9 + log 3x
Therefore: 6x^2 - (2-x) = -log9

6x^2 - 2 - x + log 9 = 0

I give up

3^2x = 4^(2-x)
2x.log3 = (2-x).log4
log3/log4 = (2-x)/(2x)
0.79248.... = (2-x)/(2x)
1.584962501x = 2-x
2.584962501x = 2
x = 2/2.584962501
x = 0.774 (3dp)
9. 3^2x=4^2-x
2xln3=(2-x)ln4
2xln3+xln4=2ln4
x(2ln3+ln4)=2ln4
x = 2ln4/(2ln3+ln4)

but i dont have a calculator to check that
10. nas you want to take logs to the base 10 usually, so your calculator can do it
11. v.true. However, i didnt think sarah liked my method with lg, log to the base 3 and 4 makes gets rid of the nasty bits of the equation. Just thinking maybe something may come out of it which would solve the question.. unlucky though
12. (Original post by sarah12345)
solve 3^(2x)=4^(2-x)
3^(2x) = 4^(2-x)
---> 2xln3 = (2-x)ln4
---> 2x/(2-x) = ln4/ln3
---> (2xln3)/(ln4) = 2-x
---> x(2ln3/ln4) = 2-x
---> (2-x)/x = ln9/ln4
---> 2/x - 1 = ln9/ln4
---> 2/x = (ln9/ln4) + 1
---> x/2 = 1/[(ln9/ln4) + 1]
---> x = 2/[(ln9/ln4) + 1]
---> x = 0.774 (3.S.F)

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Updated: February 9, 2005
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