Question

if 3^a=5^-b=15^c prove that 1/a- 1/b- 1/c=0​

Answer 1

Let 3^a= 5^-b = 15^c = k

Now (3 ^ a )1/a = k ^1/a

3= k^1/a

similarly, 5= k^-1/b and

15 = k^1/c

Now

15 = 3×5

k^1/c = k^1/a × k^-1/b

Since bases are same we can compare both sides

1/c = 1/a -1/b

1/a -1/b -1/c = 0

Hence proved.