What is the number of real values of the para | vedclass

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(B) Let $y = \log_{16}x$. The equation becomes $y^2 - y + \log_{16}k = 0$.For this quadratic equation in $y$ to have exactly one solution for $x$,it m

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$1$

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(B) Let $y = \log_{16}x$. The equation becomes $y^2 - y + \log_{16}k = 0$.For this quadratic equation in $y$ to have exactly one solution for $x$,it must have either a repeated root for $y$ or one root that leads to a valid $x$ while the other does not (but here,any real $y$ gives a valid $x = 16^y > 0$).Thus,the quadratic equation must have a discriminant $D = 0$ for a unique solution.$D = (-1)^2 - 4(1)(\log_{16}k) = 0$.$1 - 4\log_{16}k = 0$.$4\log_{16}k = 1$.$\log_{16}k = \frac{1}{4}$.$k = 16^{1/4} = (2^4)^{1/4} = 2$.Since there is only one such value of $k$,the number of real values is $1$.

What is the number of real values of the parameter $k$ for which the equation $({\log _{16}}x)^2 - {\log _{16}}x + {\log _{16}}k = 0$ has exactly one solution,given that the coefficients are real?

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