ISI2017-DCG-9

Question

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

• A. $2$
• B. $4$
• C. $5$
• D. none of these

Comments

is it d?

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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,

$\Rightarrow x+5+25-10\sqrt{x+5} = x$

$\Rightarrow 30 = 10\sqrt{x+5}$

$\Rightarrow x = 4$

Answer 1

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.

Answer 2

RHS =1 = Log 5 base 5

equating the corresponding terms and solving we get x=4

hence the option B is correct.