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2 votes
2 votes

The solution of $\log_5(\sqrt{x+5}+\sqrt{x})=1$ is

  1. $2$
  2. $4$
  3. $5$
  4. none of these
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2 Answers

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.
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.

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