11. 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(mn)=logb(m)−logb(n) to simplify the left side of the equation.
log(2x+1)-log(x-2)=1log(2x+1)−log(x−2)=1
log((2x+1)/(x-2))=1log(2x+1x−2)=1
22. Use the log property, log_color(purple)b(color(purple)b^color(orange)x)=color(orange)xlogb(bx)=x, to rewrite the right side of the equation.
log((2x+1)/(x-2))=log(10)log(2x+1x−2)=log(10)
33. Since the equation now follows a "log=loglog=log" situation, where the bases are the same on both sides of the equation, rewrite the equation without the "log" portion.
(2x+1)/(x-2)=102x+1x−2=10
44. Solve for xx.
2x+1=10(x-2)2x+1=10(x−2)
2x+1=10x-202x+1=10x−20
8x=218x=21
color(green)(|bar(ul(color(white)(a/a)x=21/8color(white)(a/a)|)))
