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Find \(\frac{a}{b}\) when \(2\log{(a -2b)} = \log{a} + \log{b}. \)

 

----------Thanks! cheeky

 May 12, 2020
 #1
avatar+26945 
+1

log (a-2b)2 = log(ab)

(a-2b)2 = ab

a^2 - 4ab+4b^2 = ab

a^2 - 5 ab + 4 b^2 = 0

(a-4b)(a-b) = 0       a = 4b       or    a = b         a/b = 4     or   1    ( I think!)   

                                    1 will not work because you would wind up with a log of a  negative in the first term ......

 May 12, 2020
 #2
avatar
-1

Stop trying to cheat on your homework.

 May 12, 2020

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