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

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

recategorized | 17 views
0
is it d?
0
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 $B$

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.
by Boss (13.3k points)