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  4. The solution of the equation log7(log5(√x +5 +√x)) =0is x =

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Q. The solution of the equation $log_{7}\left(log_{5}\left(\sqrt{x +5} +\sqrt{x}\right)\right) =0$is $x =$

Linear Inequalities

Solution:

The given equation is
$log_{7}\left[log_{5}\left(\sqrt{x +5} +\sqrt{x}\right)\right] =0$
$\Rightarrow log_{5}\left(\sqrt{x +5} +\sqrt{x}\right) =1$
$\Rightarrow \sqrt{x +5} +\sqrt{x =5}$
$\Rightarrow \sqrt{x +5} =5 -\sqrt{x}$
$\Rightarrow x+5 = 25 -10 \sqrt{x} +x$
$\Rightarrow 10\sqrt{x} =20$
$\Rightarrow \sqrt{x} =2$
$\Rightarrow x =4$
Hence, the solution is $x = 4$