The-number-of-solutions-of-the-equation-log-101-log-7-x-7-x-0-is-

Question Number 22745 by Sahib singh last updated on 22/Oct/17

The number of solutions of the

equation \log_{101} \log_{7} (\sqrt{x + 7} + \sqrt{x}) = 0 is

Answered by mrW1 last updated on 22/Oct/17

\log_{101} \log_{7} (\sqrt{x + 7} + \sqrt{x}) = 0

\Rightarrow \log_{7} (\sqrt{x + 7} + \sqrt{x}) = 1

\Rightarrow \sqrt{x + 7} + \sqrt{x} = 7

\Rightarrow \sqrt{x + 7} = 7 - \sqrt{x}

\Rightarrow x + 7 = 49 + x - 14 \sqrt{x}

\Rightarrow \sqrt{x} = 3

\Rightarrow x = 9

\Rightarrow only one solution

Commented by Sahib singh last updated on 22/Oct/17

thanks