Question

Logx base 2+logxcube base 8. =4:then x=?

Answer 1

$log_{2}(x) + log_{8}( {x}^{3} ) \: = 4 \\ \\ by \: using \: log \: properties \\ \\ log_{2}x \: + log_{2^{3} }( {x}^{3} ) = 4 \\ \\ log_{2}x \: + 3 \div 3 log_{2} \: {x} = 4 \\ \\ log_{2}x \: + log_{2} \: {x} = 4 \\ \\ 2 log_{2}(x) = 4 \\ \\ log_{2}(x) = 4 \div 2 \\ \\ log_{2}(x) = \: 2 \\ \\ by \: using \: property \: of \: log \: which \: is \ \\ log_{e}(x) = y \\ x = {e}^{y} \\ \\ therefore \\ log_{2}(x) = \: 2 \\ x = {2}^{2} \\ x = 4$