+0  
 
0
49
1
avatar

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

Guest Mar 27, 2018
Sort: 

1+0 Answers

 #1
avatar+85759 
+1

\(2\log{(a -2b)} = \log{a} + \log{b} \)

 

We can write

 

log (a - 2b)^2  = log ( a * b)

 

And we can solve

 

(a - 2b)^2  =  ab

a^2 - 4ab + 4b^2  = ab

a^2 - 5ab + 4b^2  = 0     factor

 

(a - 4b) ( a - b)  =  0

 

Setting  each factor to 0  and solving we have that

 

a  = 4b         and  a  = b

 

Assuming  a, b   are both positive, the first solution is the only one where all logs are defined for real numbers

 

So

 

a  / b  =

 

[4b]/ b  =

 

4

 

 

cool cool cool

CPhill  Mar 27, 2018

39 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details