# Solve for x and y; if x>o and y>0: log xy= lof x/y +2 log 2 = 2

2
by samharsh

2015-02-21T21:42:31+05:30

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log xy= log x/y +2 log 2 = 2

taking the first two;
log xy= lof x/y +2 log 2
⇒ log x + log y = log x - log y + 2 log 2
⇒ log y = -log y + 2 log 2
⇒ 2 log y = 2 log 2
⇒ y = 2

taking first and third;
log xy = 2
⇒ log 2x = 2
⇒ 2x = 10² = 100
⇒ x = 100/2 = 50

x = 50, y = 2

2015-02-23T01:24:29+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Let us say that the base of the logarithm is 10.

Log x/y + 2 Log 2 = 2 =  2 * Log 10
Log x/y = 2 Log 10 - 2 Log 2  = Log 10² - Log 2² = Log 10²/2² = Log 25
x/y = 25    => x = 25 y

Log xy = 2      =>    Log 25y² = 2
=>  Log (5y)² = 2     =>  2 Log (5y) = 2
Log 5y =1
5 y = 10     => y = 2
x = 50

verification:

Log xy = Log 100  =2  ;  log x/y + 2 Log 2  = Log 25 + Log 4 = Log 100 = 2