Question

The solution of the equation $lo{g}_{7}lo{g}_5\left(\sqrt{x^2+5+x}\right)=0$

• A. x = 2
• B. x = 3
• C. x = 4
• D. x =-2

Answer 1

The correct option is C x = 4

$lo{g}_{7}lo{g}_5\left(\sqrt{x^2+5+x}\right)=0$
$\Rightarrow lo{g}_5(x^2+5+x{)}^{\frac{1}{2}}=1$
$\Rightarrow (x^2+5+x{)}^{\frac{1}{2}}=5$
$\Rightarrow (x^2+x+5)=25\Rightarrow x^2+x-20=0$
$\Rightarrow (x-4)(x+5)=0\Rightarrow x=4,-5\Rightarrow x=4$