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avatar+93 

Find \(a/b\) when \(2\log{(a -2b)}\)\(\log{a} + \log{b}\)

 Apr 4, 2020
edited by littlemixfan  Apr 4, 2020
 #1
avatar+20876 
+1

2log(a - 2b)  =  log(a) + log(b)

Using properties of logs:

--->          log(a - 2b)2  =  log(a·b)

--->               (a - 2b)2  =  ab

--->      a2 - 4ab + 4b2  =  ab

--->      a2 - 5ab + 4b2  =  0

--->        (a - 4b)(a - b)  =  0

 

Either  a - 4b  =  0   --->   a = 4b   --->   a/b  =  4

or          a - b  =  0   --->   a  =  b     [but this is impossible for it would make a - 2b negative]

 Apr 4, 2020
 #2
avatar+93 
+1

Thank you so much!

littlemixfan  Apr 4, 2020

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