Solution of equation {log g}{log ₅} (√ {{x^2} + 5 + x} ) = 0

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Basic of Logarithms

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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

$x = - 2$

Solution

(c) ${\log _7}{\log _5}(\sqrt {{x^2} + 5 + x} ) = 0 = {\log _7}1$

$ \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$ ==> $x = 4$.

Standard 11

Mathematics

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