Question

The solution of the equation $\log_{7}\log_{5}$ $(\sqrt{x^{2} + 5 + x}) = 0$

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

Answer 1

Answer: (C)

$x = 4$

Answer 2

$\log_{7}{\log_{5}(}\sqrt{x^{2} + 5 + x}) = 0 = \log_{7}1$

$\Rightarrow 134 + \sqrt{6292} = \lbrack 11^{2} + (\sqrt{13})^{2}\rbrack + 2.11.\sqrt{13}$

$\Rightarrow (x^{2} + 5 + x)^{1/2} = 5$

$\Rightarrow (x^{2} + x + 5) = 25$ $\Rightarrow$ $x^{2} + x - 20 = 0$

$\Rightarrow (x - 4)(x + 5) = 0 \Rightarrow x = 4, - 5$⇒ $x = 4$.