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Plummie
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#1
Report Thread starter 12 years ago
#1
I feel really stupid because i'm certain that this question is really easy i just can't do it right now. Would be really grateful if you could show/explain how to get the answer. It's the fact that ^x is on both sides that has me stumped.

4^x+2=5^x
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the_anomaly
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#2
Report 12 years ago
#2
Assuming you mean 4^(x+2) = 5^x.....

log (4^(x+2)) = log(5^x)

(x+2)log4 = xlog5

xlog4 + 2log4 = xlog5

x(log5 - log4) = 2log4

x = 2log4/(log5 - log4)
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Jonny W
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#3
Report 12 years ago
#3
If you don't like x being on both sides, divide by 4^x:

16 = (5/4)^x

That kind of equation should be more familiar
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Plummie
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#4
Report Thread starter 12 years ago
#4
thanks, i knew it was something simple, just too addled to get it
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sea tea
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#5
Report 12 years ago
#5
if its 2 + 4^x = 5^x, no idea. use an iteration to solve it. if on the other hand you meant 4(x+2) = 5x then its some simple log work.

4(x+2) = 5x
(x+2) ln4 = x ln5
x(ln4 - ln5) = 2 ln4
x = {ln16/ln0.8}
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yazan_l
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#6
Report 12 years ago
#6
how did you get the third line from the 2nd one?
(x+2) ln4 = x ln5
xln4 + 2ln4 = xln5
xln4 - xln5 = -2ln4
x(ln4-ln5) = -2ln4

Edit:
forgot to continue!:
x(ln4-ln5) = -2ln4
-x(ln4-ln5) = 2ln4
x(ln5-ln4) = 2ln4
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yazan_l
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#7
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#7
haha... well i hate it when this "moment" comes while i'm in the exam!! :rolleyes:
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yazan_l
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#8
Report 12 years ago
#8
hoho.. trust me: it did (to me)! A LOT!
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yazan_l
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#9
Report 12 years ago
#9
haha... EVERY one...
VERY stupid mistakes!
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