First slide

Types of real valued functions XI

Question

If $p > 1 and q > 1$ are such that $\log (p + q) = \log p + \log q$ then the value of $\log (p - 1) + \log (q - 1)$ is equal to

Moderate

A

0
B

1
C

2
D

none of these

Solution

$\begin{array}{l} \log (p + q) = \log p + \log q \\ \Rightarrow p + q = pq \\ \Rightarrow pq - p - q = 0 \\ \Rightarrow pq - p - q + 1 = 1 \\ \Rightarrow (p - 1) (q - 1) = 1 \\ \Rightarrow \log (p - 1) + \log (q - 1) = \log 1 = 0 \end{array}$

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