Question

If 2log4X = 1 + log4(X-1) , then find the value of X .

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Answer 1

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Your Question :-
$= > \: \: 2log_{4}(x) \: = \: 1 \: + \: log_{4}(x - 1) \\ = > log_{4}(x {}^{2} ) - \: log_{4}(x - 1) = 1 \\ \\ = > \: log_{4}( \frac{x {}^{2} }{x - 1} ) \: = 1 \\ = > 4 {}^{1} = \frac{x {}^{2} }{(x - 1)} \\ = > x {}^{2} = 4x - 4 \\ this \: becomes \: quadratic \: equation \: \\ = > x {}^{2} - 4x + 4 = 0 \\ = > (x - 2) {}^{2} = 0 \\ = > > \: \: x = 2$

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