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# Logarithms

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

----------Thanks!

May 12, 2020

#1
+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
-1

Stop trying to cheat on your homework.

May 12, 2020