#1#. Since the left and right sides of the equation do not have the same base, start by taking the log of both sides.
#16^(x-4)=3^(3-x)#
#log(16^(x-4))=log(3^(3-x))#
#2#. Use the log property, #log_color(purple)b(color(red)m^color(blue)n)=color(blue)n*log_color(purple)b(color(red)m)#, to simplify both sides of the equation.
#(x-4)log16=(3-x)log3#
#3#. Expand the brackets.
#xlog16-4log16=3log3-xlog3#
#4#. Group all like terms together such that the terms with the variable, #x#, are on the left and the ones without on the right.
#xlog16+xlog3=3log3+4log16#
#5#. Factor out #x# from the terms on the left side of the equation.
#x(log16+log3)=3log3+4log16#
#6#. Solve for #x#.
#x=(3log3+4log16)/(log16+log3)#
#color(green)(|bar(ul(color(white)(a/a)x~~3.72color(white)(a/a)|)))#
