#1#. Since the left and right sides of the equation do not have the same base, start by taking the log of both sides.
#3^(x-8)=8^x#
#log(3^(x-8))=log(8^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-8)log3=xlog8#
#3#. Expand the brackets.
#xlog3-8log3=xlog8#
#4#. Group all like terms together such that the terms with the variable, #x#, are on the left side and #8log3# is on the right side.
#xlog3-xlog8=8log3#
#5#. Factor out #x# from the terms on the left side of the equation.
#x(log3-log8)=8log3#
#6#. Solve for #x#.
#x=(8log3)/(log3-log8)#
#color(green)(|bar(ul(color(white)(a/a)x~~-8.96color(white)(a/a)|)))#
