if log(x+y/3)=1/2(logx+logy)
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Then x/y + y/x =7
log (x+y/3) = 1/2 (log x + log y)
log (x+y/3) = (log x + log y)^
log (x+y/3) = (log xy)^
cancel log on both sides
(x+y/3) = (xy)^
squaring on both sides
(x+y)^/3^ = xy
(x+y)^/9 = xy
(x+y)^ = 9xy
x^ + y^+ 2xy = 9xy
x^ + y^ = 9xy - 2xy
x^ + y^ =7xy
x^ + y^/ xy = 7
x^/xy + y^/xy = 7
x / y + y / x =7
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