How do you condense #3 ln 3 + ln 9#?

1 Answer
Apr 6, 2016

Answer:

#ln243#

Explanation:

#1#. Start by using the natural logarithmic property, #ln_color(purple)b(color(red)m^color(blue)n)=color(blue)n*ln_color(purple)b(color(red)m)#, to simplify #3ln3#.

#3ln3+ln9#

#=ln(3^3)+ln(9)#

#2#. 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)#, to simplify the expression.

#=ln(3^3*9)#

#3#. Simplify.

#=ln(27*9)#

#=color(green)(|bar(ul(color(white)(a/a)ln243color(white)(a/a)|)))#