If p >= 0 and p^q = p^(r-1) = q^r, what is the value of the product p*q*r? A. -1 B. 1/p^r C. 1 D. p*q^r

GATE 2018 · General Aptitude · Logarithms · medium

Answer: The value of the product p*q*r = 1. Answer: C.

1. Equate first two expressions: If log(p) != 0 (p != 1), then q = r-1. If p=1, then both sides = 1 for any q,r, and q^r must also equal 1, forcing q=1, giving r=1 (from q=r-1 => 1=0, contradiction). So the non-trivial case requires checking p^q=q^r.
2. Verify p=q=r=1: All three expressions equal 1. The product p*q*r = 1*1*1 = 1.