11. Start by using the natural logarithmic property, ln_color(purple)b(color(red)m/color(blue)n)=ln_color(purple)b(color(red)m)-ln_color(purple)b(color(blue)n)lnb(mn)=lnb(m)−lnb(n) to simplify the left side of the equation.
ln(y-7)-ln(7)=x+ln(x)ln(y−7)−ln(7)=x+ln(x)
ln((y-7)/7)=x+ln(x)ln(y−77)=x+ln(x)
22. Use the natural logarithmic property, ln_color(purple)b(color(purple)b^color(orange)x)=color(orange)xlnb(bx)=x, to rewrite xx on the right side of the equation.
ln((y-7)/7)=ln(e^x)+ln(x)ln(y−77)=ln(ex)+ln(x)
33. Use the natural logarithmic property, ln_color(purple)b(color(red)m*color(blue)n)=ln_color(purple)b(color(red)m)+ln_color(purple)b(color(blue)n)lnb(m⋅n)=lnb(m)+lnb(n) to simplify the right side of the equation.
ln((y-7)/7)=ln(e^xln(y−77)=ln(exx)x)
44. Since the equation now follows a "ln=lnln=ln" situation, where the bases are the same on both sides, rewrite the equation without the "lnln" portion.
(y-7)/7=e^(x)xy−77=exx
55. Solve for yy.
y-7=e^(x)7xy−7=ex7x
color(green)(|bar(ul(color(white)(a/a)y=e^(x)7x+7color(white)(a/a)|)))
