If log1281 = p, then 34-p4+p is equal to
Explanation:
log1281 = p
⇒ p = 4log123
Now, 4-p4+p=4-4log1234+4log123
= 1-log1231+log123
= log1212-log123log1212+log123=log1212/3log1212×3=log124log1236
= 2log1222log126 = log62
Hence, 34-p4+p=3log62=log68
Alternately, log1281 = p ⇒ 81 = 12p ⇒ 34 = 3p × 22p ⇒ 3(4 − p) = 22p
Taking log on both the sides,
(4 – p) (log 3) = (2p) (log 2)
∴ log3log2 = 2p4-p
∴ log3+log2log2 = 2p + (4-p)4-p …(by adding 1 both sides)
∴ log6log2 = 4+p4-p
∴ 4-p4+p = log2log6 = log62
∴ 34-p4+p = 3log62 = log68
Hence, option (c).
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.