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)|)))
