The solution of the equation log _{101} log _ | vedclass

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(C) Given, $\log _{101} \log _{7}(\sqrt{x+7}+\sqrt{x})=0$ $	herefore \log _{7}(\sqrt{x+7}+\sqrt{x}) = (101)^{0} = 1$ $\Rightarrow \sqrt{x+7}+\sqrt{x}

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$9$

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(C) Given, $\log _{101} \log _{7}(\sqrt{x+7}+\sqrt{x})=0$ $	herefore \log _{7}(\sqrt{x+7}+\sqrt{x}) = (101)^{0} = 1$ $\Rightarrow \sqrt{x+7}+\sqrt{x} = 7^{1} = 7$ Squaring both sides, we get: $(\sqrt{x+7}+\sqrt{x})^{2} = 7^{2}$ $x+7+x+2\sqrt{x(x+7)} = 49$ $2x+7+2\sqrt{x^{2}+7x} = 49$ $2\sqrt{x^{2}+7x} = 42-2x$ $\sqrt{x^{2}+7x} = 21-x$ Squaring both sides again: $x^{2}+7x = (21-x)^{2}$ $x^{2}+7x = 441 - 42x + x^{2}$ $7x = 441 - 42x$ $49x = 441$ $x = \frac{441}{49} = 9$

The solution of the equation $\log _{101} \log _{7}(\sqrt{x+7}+\sqrt{x})=0$ is

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