If 5 – log101+x + 4log101-x = log1011-x2, then 100x equals
Explanation:
Given, 5 – log101+x + 4log101-x = log1011-x2
⇒ 5 – log101+x1/2 + log101-x4/2 = log101-x2-1/2
⇒ 5 = log101+x1/2 - log101-x2 - log101-x21/2
⇒ 5 = log101+x1/2(1-x)2×{(1+x)(1-x)}1/2
⇒ 5 = log10(1-x)-5/2
⇒ 5 = -5/2 × log10(1 - x)
⇒ -2 = log10(1 - x)
⇒ 1 – x = 10-2 = 1/100
⇒ 100 – 100x = 1
⇒ 100x = 99
Hence, 99.
» Your doubt will be displayed only after approval.
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.