Question

$log _{6}( x^{2} +x) = log _{2} x$

Answer 1

log[tex] log_{6} (x^{2}+x) = log_{2}x \\ \frac{log _{2}x(x+1) }{ log_{2}6} = log_{2}x \\ log_{2}x + log_{2}(x+1)= log_{2}x(log_{2}3+log_{2}2) \\ log_{2}x + log_{2}(x+1)=log_{2}3x+log_{2}x \\ log_{2}(x+1)=log_{2}3x => \\ x+1=3x \\ 2x=1\\ x= \frac{1}{2} \\ \\ c.e.: x > 0;(1) x(x+1) > 0;(2) din (1), (2) => x > 1[/tex]
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