If logr 6 = m and logr 3 = n, then what is logr (\(\frac{r}{2}\)) equa

1.	If logr 6 = m and logr 3 = n, then what is logr (\(\frac{r}{2}\)) equal to ?(a) m – n + 1 (b) m + n – 1 (c) 1 – m – n (d) 1 – m + n
Answer» (d) 1 - m + n. Given, log_r 6 = m and log_r 3 = n Since, log_r 6 = log_r (2 × 3) = log_r 2 + log_r 3 ⇒ log_r 2 + log_r3 = m ⇒ log_r 2 + n = m ⇒ log_r 2 = m – n Now, logr (\(\frac{r}{2}\)) = log_r r – log_r2 = 1 – (m – n) = 1 – m + n.

If logr 6 = m and logr 3 = n, then what is logr (\(\frac{r}{2}\)) equal to ?(a) m – n + 1 (b) m + n – 1 (c) 1 – m – n (d) 1 – m + n

Answer»

(d) 1 - m + n.

Given, log_r 6 = m and log_r 3 = n

Since, log_r 6 = log_r (2 × 3) = log_r 2 + log_r 3

⇒ log_r 2 + log_r3 = m

⇒ log_r 2 + n = m ⇒ log_r 2 = m – n

Now, logr (\(\frac{r}{2}\)) = log_r r – log_r2 = 1 – (m – n) = 1 – m + n.