Allen Career Institute: Aptitude

Question

If $log_{4}\left ( \frac{2}{x} \right )+log_{16}\left ( 0.5 \right )=2$ then

$(A)$ $4log_{4}x=-7$

$\left ( B \right )2log_{4}x=-7$

$\left ( C \right )2log_{16}x=-7$

$\left ( D \right )log_{16}x=-7$

Answer 1

Answer should be (A)

Explanation:

$\log_{4}2 - \log_{4}x + (\log_{16}(1/2)) = 2$

$\log_{4}4^{1/2} - \log_{4}x + (\log_{16}1 - \log_{16}2) = 2$

$1/2 - \log_{4}x + (0 - \log_{16}16^{1/4}) = 2$

$1/2 - 1/4 - 2 = \log_{4}x$

$-7/4 = \log_{4}x$

$4log_{4}x = -7$