2 votes 2 votes The solution of $\log_5(\sqrt{x+5}+\sqrt{x})=1$ is $2$ $4$ $5$ none of these Quantitative Aptitude isi2017-dcg quantitative-aptitude logarithms + – gatecse asked Sep 18, 2019 recategorized Nov 15, 2019 by Lakshman Bhaiya gatecse 433 views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Ashwani Kumar 2 commented Sep 19, 2019 reply Follow Share is it d? 0 votes 0 votes ankitgupta.1729 commented Sep 19, 2019 reply Follow Share answer should be $B$. It can be easily check by putting $x=4$ $log_{5}(\sqrt{x+5} + \sqrt{x}) = 1$ $\Rightarrow \sqrt{x+5} + \sqrt{x} = 5 $ $\Rightarrow \sqrt{x+5} - 5 = -\sqrt{x} $ On squaring both sides, $\Rightarrow x+5+25-10\sqrt{x+5} = x$ $\Rightarrow 30 = 10\sqrt{x+5}$ $\Rightarrow x = 4$ 2 votes 2 votes Please log in or register to add a comment.
1 votes 1 votes Answer $B$ Given: $$\log_5(\sqrt{x+5} + \sqrt{x}) = 1$$ Now, Substitute $x = 4$, we get: $$\log_5(\sqrt{4+5} + \sqrt{4}) = \log_5(\sqrt9+\sqrt4) = \log_55 = 1, \;as\; \log_aa= 1$$ $\therefore \; B$ is the right answer. `JEET answered Sep 28, 2019 `JEET comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes RHS =1 = Log 5 base 5 equating the corresponding terms and solving we get x=4 hence the option B is correct. DIBAKAR MAJEE answered May 3, 2020 DIBAKAR MAJEE comment Share Follow See all 0 reply Please log in or register to add a comment.