11. Use the log property, log_color(purple)b(color(red)m^color(blue)n)=color(blue)n*log_color(purple)b(color(red)m)logb(mn)=n⋅logb(m), to rewrite 2log_(9)52log95.
log_(9)4+2log_(9)5=log_(9)wlog94+2log95=log9w
log_(9)4+log_(9)5^2=log_(9)wlog94+log952=log9w
22. Use the log property, log_color(purple)b(color(red)m*color(blue)n)=log_color(purple)b(color(red)m)+log_color(purple)b(color(blue)n)logb(m⋅n)=logb(m)+logb(n) to simplify the left side of the equation.
log_(9)(4*5^2)=log_(9)wlog9(4⋅52)=log9w
log_(9)(100)=log_(9)wlog9(100)=log9w
33. Since the equation now follows a "log=loglog=log" situation, where the bases are the same on both sides, rewrite the equation without the "log" portion.
100=w100=w
color(green)(|bar(ul(color(white)(a/a)w=100color(white)(a/a)|)))
