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Q)

Solve :$\log _7\log _5(\sqrt{x+5}+\sqrt{x})=0$

$(a)\;2\qquad(b)\;3\qquad(c)\;4\qquad(d)\;5$

1 Answer

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A)
Step 1:
$\log_7[\log_5(\sqrt{x+5}+\sqrt x)]=0$
$\log_5(\sqrt{x+5}+\sqrt x)=7^{\large\circ}$
$[\log_aN=k\Rightarrow a^k=N]$
$\log _5(\sqrt{x+5}+\sqrt{x})=1$
$\sqrt{x+5}+\sqrt x=5^1=5$
$\sqrt{x+5}=5-\sqrt x$
Step 2:
Squaring we get,
$x+5=25+x-10\sqrt x$
$10\sqrt x=20$
$\sqrt x=\large\frac{20}{10}$
$\sqrt x=2$
$x=4$
Hence (c) is the correct answer.
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