Question

 If log₆ 161 = a, log₆ 23 = b, what is the value of log₇ 6 in terms of a and b? 
1. a/b
2. 1/(a - b)
3. a + b
4. b/a

Answer 1

Correct Answer - Option 2 : 1/(a - b)

Calculation :

Given, a = log₆ 161 = log₆ (23 × 7)

= log₆ 23 + log₆ 7

also giiven, b = log₆ 23

⇒ a = b + log₆ 7

⇒ a - b = log₆ 7

⇒ log₇ 6 = 1/(a - b)

In this type of question always try to factorize value inside the log and then use these formulas:

log(p × q) = log(p) + log(q)

log(p/q) = log(p) - log(q)