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algebra intermediate

Problem

lo g p + lo g q = lo g (p + q)

only if:

(A)

p = q = z er o

(B)

p = \frac{q ^{2}}{1 - q}

(C)

p = q = 1

(D)

p = \frac{q}{q - 1}

Solution

lo g p + lo g q = lo g (p + q) ⟹ lo g pq = lo g (p + q) ⟹ pq = p + q ⟹ p = \frac{q}{q - 1}

Final answer

D