+0

0
50
1
+79

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

Apr 18, 2021

#1
+325
0

$$2\log{(a -2b)} = \log{a} + \log{b}\\ \log((a-2b)^2)=\log(ab)\\ (a-2b)^2=ab\\ a^2-4ab+4b^2=ab\\ a^2-5ab+4b^2=0\\$$

You can factor this polynomial like this:

$$(a-4b)(a-b)=0$$

So the two solutions for a/b are:

$$a-4b=0\\a=4b\\ \boxed{\frac{a}{b}=4}$$

and

$$a-b=0\\a=b\\\boxed{\frac{a}{b}=1}$$

Apr 18, 2021