If 5^-p = 4^-q = 20^r, show that : 1/p + 1/q + 1/r = 0 .

Question

KnowledgeBoat · Accepted Answer

Given, ⇒ 5^-p = 4^-q = 20^r = k (let) ⇒ 5^-p = k ⇒ 5 = .......(1) ⇒ 4^-q = k ⇒ 4 = ......(2) ⇒ 20^r = k ⇒ 20 = ............(3) We know that, ⇒ 5 × 4 = 20 From equations (1), (2) and (3), we get : Hence, proved that .

Mathematics

If 5^-p = 4^-q = 20^r, show that : 1/p + 1/q + 1/r = 0 .

Indices

Related Questions

If a^x = b, b^y = c and c^z = a, prove that :
xyz = 1.

If m ≠ n and (m + n)^-1 (m^-1 + n^-1) = m^xn^y;
show that : x + y + 2 = 0

If 5^{x + 1} = 25^{x - 2}; find the value of :
3^{x - 3} × 2^{3 - x}.

Mathematics

If 5^-p = 4^-q = 20^r, show that : 1/p + 1/q + 1/r = 0 .

Indices

Related Questions

If ax = b, by = c and cz = a, prove that :xyz = 1.

If m ≠ n and (m + n)-1 (m-1 + n-1) = mxny;show that : x + y + 2 = 0

If 5x + 1 = 25x - 2; find the value of :3x - 3 × 23 - x.

If a^x = b, b^y = c and c^z = a, prove that :
xyz = 1.

If m ≠ n and (m + n)^-1 (m^-1 + n^-1) = m^xn^y;
show that : x + y + 2 = 0

If 5^{x + 1} = 25^{x - 2}; find the value of :
3^{x - 3} × 2^{3 - x}.