Question

Find x if log x to the base 2+ log x to the base 4+ log x to the base 16= 21/4

Answer 1

$\frac{21}{4} = log_{2}(x) + log_{ {2}^{2} }(x) + log_{ {x}^{4} }(x) \\ log_{2}(x) (1 + \frac{1}{2} + \frac{1}{4} ) = \frac{21}{4} \\ log_{2}(x) ( \frac{7}{4} ) = \frac{21}{4} \\ log_{2}(x) = \frac{21 \times 4}{7\times 4} \\ x = {2}^{3 } \\ x = 8$