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(log√125 + log √27  √8)/ log 15  log 2 = 3/2 
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#1
Nov1612, 01:32 AM

P: 523

1)Without using tables, show that
(log√125 + log √27  √8)/ log 15  log 2 = 3/2 What i tried was (3/2 log 5 + 3/2 log 3  3/2 log 2)/ log 5+log 3  log2 then from here I don't know where to take it. 2) Find the value of x if log x^{2}/ log a^2 = log y^4/logy I tried this 2logx  2loga = 4 log y log y 2logx = 3logy+ 2 loga then here I get stuck.. 


#2
Nov1612, 01:43 AM

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ehild 


#3
Nov1612, 01:43 AM

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[tex]\log(x)=y[/tex] then what is x? 


#4
Nov1612, 01:45 AM

P: 523

(log√125 + log √27  √8)/ log 15  log 2 = 3/2
10^y = x?



#5
Nov1612, 01:52 AM

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Yes, so now do the same thing. Set the equation so that it is in the form [itex]\log(x)=y[/itex] and then make x the subject. Oh and y will be some complicated expression.
And once you've done that, remember the rules [tex]a^{x+y}=a^xa^y[/tex] [tex]a^{\log_{a}(x)}=x[/tex] 


#6
Nov1612, 02:01 AM

P: 523

I'm kind of confused if I have this
log x = 3logy  2loga I duno how to get rid of log a to make it log (x) = y 


#7
Nov1612, 02:04 AM

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ehild 


#8
Nov1612, 02:13 AM

P: 523

oh.. so it's 2log x = 4 + 2log a
x^2= a^8 x=a^4? 


#9
Nov1612, 02:15 AM

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[tex]\frac{\log(a)}{\log(b)}\neq \log(a)\log(b)[/tex] What you're thinking of is [tex]\log\left(\frac{a}{b}\right)=\log(a)\log(b)[/tex] 


#10
Nov1612, 02:19 AM

P: 523

Oh, Umm should it should be
log x^2/ log a^2 = 4 2log x = 8 log a log x = 4log a 10^a^4 = 10^x x= a^4? 


#11
Nov1612, 02:43 AM

P: 523

And for the first one
is it (3/2log5 + 3/2log 3  3/2log 2)/ (log 5+ log 3)  log 2 = 1/2log log + 1/2log 3  1/2log2? 


#12
Nov1612, 04:41 AM

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I think you made some mistake when copying the problem. It should be
(log√125 + log √27  √8)/ (log 15  log 2 )= 3/2. ehild 


#13
Nov1612, 09:26 AM

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#14
Nov1712, 02:19 AM

P: 523

I still don't get it combine them? But aren't they too big? shouldn't I try to get them down to like small numbers and then try to cancel out?



#15
Nov1712, 02:47 AM

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Use [tex]\log(a)+\log(b)\log(c)=\log\left(\frac{ab}{c}\right)[/tex] for both the numerator and denominator and see if you notice any nice cancellations. 


#16
Nov1712, 02:50 AM

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How about the first one should be: (log√125 + log √27  log√8)/ (log 15  log 2 )= 3/2 As ehild said early on, you need to use sufficient parentheses . 


#17
Nov1712, 05:04 PM

P: 523

thank you guys.



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