Question

Solution of $lo{g}_{7}lo{g}_5(\sqrt{x+5}+\sqrt{x})=0$ is

• A. x = 2
• B. x = 5
• C. x = - 5
• D. x = 4

Answer 1

The correct option is D x = 4

Consider the given equation.

$lo{g}_{7}lo{g}_5(\sqrt{x+5}+\sqrt{x})=0$
$lo{g}_5(\sqrt{x+5}+\sqrt{x})=7^0=1$
$\sqrt{x+5}+\sqrt{x}=5^1=5$
$\sqrt{x+5}=5-\sqrt{x}$
On squaring both sides, we get
$x+5=25+x-10\sqrt{x}$
$\sqrt{x}=2$
$x=4$
Hence, this is the answer.