Question

If 2^a =3^b =6^c then show that c = ab÷a+b

Answer 1

If 2^a =3^b =6^c , then prove that c = ab / a+b

there may be other ways to solve it. and my ans is correct but u may not get full marks. i m not sure.

let 2^a =3^b =6^c = d

so, 2^a = d

=>d^(1/a) = 2--------(1)

and 3^b =d

=>d^(1/b)=3---------(2)

and also 6^c=d

=>d^(1/c)=6---------(3)

we know that 6= 2X3,

6= 2X3----(4)

now put value of 2, 3 and 6 from equation 1, 2 and 3 we get

d^(1/a) × d^(1/b) = d^(1/c)

d^(1/a +1/b) = d^(1/c)

so, 1/c = 1/a+1/b =>1/c= (b+a)/ab

=> c= ab/a+b hence proved.