Question 124

$$log_{13} log_{21} (\sqrt{x+21}+ \sqrt{x} ) =0 $$ then the value of x is

Solution

$$log_{13} log_{21} (\sqrt{x+21}+ \sqrt{x} ) =0 $$
Thus, $$log_{21} (\sqrt{x+21}+ \sqrt{x} ) = 1 $$
Thus, $$(\sqrt{x+21}+ \sqrt{x} ) = 21 $$
Let, $$\sqrt{x} = t$$
Thus, $$x = t^2$$
Thus, $$x+21 = t^2+21$$
Thus, $$\sqrt{t^2+21}+t = 21$$
Thus, $$(t^2+21) = (21-t)^2$$
=> $$t^2 + 21 = 441 - 42t + t^2$$
=> $$42t = 420$$
Hence, $$t = 10$$
Hence, option D is the correct answer.

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$$log_{13} log_{21} (\sqrt{x+21}+ \sqrt{x} ) =0 $$ then the value of x is

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