Question 614561
If {{{ log((x + y)/5)}}} = {{{ log(sqrt(x))+ log(sqrt(y)) }}} where x and y are greater than 0, show that {{{ x^2 + y^2 = 23xy }}}
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log((x + y)/5)= log(sqrt(x))+ log(sqrt(y))
show that x^2 + y^2 = 23xy
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log((x + y)/5)- log(sqrt(x)- log(sqrt(y)=0
log((x + y)/5)- [(log(sqrt(x)+ log(sqrt(y)]=0
place under single log:
log[((x + y)/5)/(√x*√y)]=0
convert to exponential form:
10^0=[((x + y)/5)/(√x*√y)=1
[((x + y)/5)=(√xy)
(x + y)=5√xy
square both sides
x^2+2xy+y^2=25xy
x^2+y^2=23xy