Question

answer it fast......​

Answer 1

GOOD MORNING!

$5x {}^{ log_{2}(3) } + 3 {}^{ log_{2}(x) } = 162 \\ \\ 5 \times 3 {}^{ log_{2}(x) } + 3 {}^{ log_{2}(x) } = 162 \\ becoz \: \: a {}^{ log_{y}(t) } = t {}^{ log_{y}(a) } \\ \\ 6 \times 3 {}^{ log_{2}(x) } = 162 \\ \\ 3 {}^{ log_{2}(x) } = 27 \\ \\ taking \: log_{4} \: on \: both \: sides \: we \: have \\ \\ log_{4}(3 {}^{ log_{2}(x) } ) = log_{4}(3 {}^{3} ) \\ \\ log_{2}(x) \times log_{4}(3) = 3 \times log_{4}(3) \\ becoz \: \: \: log(x {}^{n} ) = n log(x) \\ \\ log_{2}(x) = 3 \\ \\ multiply \: both \: sides \: by \: 1 \div 2 \: we \: have \\ \\ (1 \div 2) log_{2}(x) = 3 \div 2 \\ \\ log_{2 {}^{2} }(x) = 3 \div 2 \\ becoz \: \: (1 \div n) log_{b}(z) = log_{b {}^{n} }(z) \\ \\ log_{4}(x) = 3 \div 2$