Question

if log a+b/3 = 1/2 (loga+logb) then a/b+b/a is

Answer 1

log[a+b/3]=1/2[loga+logb]

2log[a+b/3]=log[ab]

log[a+b/3]^2=log[ab]

[a+b]^2/9=ab

a^2+b^2+2ab=9ab

a^2+b^2=7ab

dividing by ab

a/b+b/a=7

hope it helps ❤️

Answer 2

Answer:

   $\frac{a}{b} + \frac{b}{a}$ = 7

Step-by-step explanation:

• Given , log($\frac{a + b}{3}$) = $\frac{1}{2}$ log(a + b)

                   2 log($\frac{a + b}{3}$) = log(a + b)..................(i)

• Now  2 log($\frac{a + b}{3}$) = log ($\frac{a + b}{3}$)²    [ as we know log($x^a$) = a × log(x)]

                                  = log($\frac{a^{2} +2ab + b^{2} }{9}$)

• log(a + b) = log(a.b)
• Putting the values in equation (i) we get,

                  log($\frac{a^{2} +2ab + b^{2} }{9}$) = log(a.b)

                    $\frac{a^{2} +2ab + b^{2} }{9}$ = ab

                    a² + 2ab + b² = 9ab

                    a² + b² = 9ab - 2ab

                      a² + b²   = 7ab

                      $\frac{a^{2} }{ab} + \frac{b^{2} }{ab}$ = 7 [both sides divided by ab]

                     $\frac{a}{b} + \frac{b}{a}$ = 7