Question

If 3^a=5^-b=15^c,Prove 1/a-1/b=1/c

Answer 1

Heya!!

3^a = 5^-b = 15^c = k ( let )

3 = k^(1/a) , 5 = k^(-1/b) And 15^c = k

15^c = k

{ 5 × 3 }^c = k

{ k^(-1/b) × k^(1/a) }^c = k

k^(-1/b) × k^(1/a) = k^(1/c)

k^(-1/b + 1/a) = k^(1/c)

Now, compare powers of k we have

(-1/b) + (1/a) = 1/c

1/c = 1/a - 1/b

1/c = 1/a - 1/b

Hence, proved.