anonymous
  • anonymous
I have to write this as a single natural logarithm. 3 ln 3 + 2 ln x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Nnesha
  • Nnesha
same like log :=)
Nnesha
  • Nnesha
power rule first :=) it's like backwards :=)
Nnesha
  • Nnesha
power rule \[\large\rm log_b x^y = y \log_b x\]

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More answers

anonymous
  • anonymous
log3 3^2 = 2 log3 3 I am so bad at these
Nnesha
  • Nnesha
let's deal with log and ln today! so you can i'm really good at it!
anonymous
  • anonymous
awesome okay
Nnesha
  • Nnesha
okay so here is an example ln and log same rules apply for both \[\rm 5 \ln y = \ln y^5\] number at front of ln becomes exponent of y
Nnesha
  • Nnesha
|dw:1440780028325:dw|
Nnesha
  • Nnesha
so how would you write \[\huge\rm 3 \ln 3 =??\] on the previous post you were expanding log equation not condense write in single ln form
anonymous
  • anonymous
as ln^3?
anonymous
  • anonymous
I'm sorry let me go back and try again thats wrong
Nnesha
  • Nnesha
okay :=)
anonymous
  • anonymous
I feel like it should be ln 3^3
Nnesha
  • Nnesha
yes right!
Nnesha
  • Nnesha
same rules apply for 2 ln x = ??
anonymous
  • anonymous
ln 2^2
Nnesha
  • Nnesha
hmm
Nnesha
  • Nnesha
there is only one `2`
anonymous
  • anonymous
oh right yeah
anonymous
  • anonymous
so just ln 2 ?
Nnesha
  • Nnesha
it's 2 ln of x |dw:1440780554920:dw|
anonymous
  • anonymous
oh okay
Nnesha
  • Nnesha
so 2 wll become exponent of x
anonymous
  • anonymous
okay
Nnesha
  • Nnesha
so how would yo write 2 ln x = ?
anonymous
  • anonymous
x^2 ?
Nnesha
  • Nnesha
yes right! but don't forget the ln so \[\huge\rm \color{reD}{3} \ln 3 +\color{blue}{ 2} \ln x \]\[\huge\rm ln 3^\color{red}{2} + \ln x^\color{blue}{2}\] now we can write it in single ln
Nnesha
  • Nnesha
there is plus sign which property you should apply ?
anonymous
  • anonymous
product rule?
Nnesha
  • Nnesha
yes right
anonymous
  • anonymous
isnt this product rule logb(x ∙ y) = logb(x) + logb(y)
anonymous
  • anonymous
so would all the logb be log3?
Nnesha
  • Nnesha
no simple log means log base 10
Nnesha
  • Nnesha
in ur question it's ln 3^3 + ln x^2
Nnesha
  • Nnesha
it's natural log you don't have to worry about the base
anonymous
  • anonymous
so just ln 9x^2 ? I think
Nnesha
  • Nnesha
yes right
anonymous
  • anonymous
oh well the last part was easier than I thought. i think I just get confused with how to simplify everything. Thank you I really appreciate you helping :)))
Nnesha
  • Nnesha
my pleasure :=)

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