I have to write this as a single natural logarithm. 3 ln 3 + 2 ln x

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I have to write this as a single natural logarithm. 3 ln 3 + 2 ln x

Mathematics
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same like log :=)
power rule first :=) it's like backwards :=)
power rule \[\large\rm log_b x^y = y \log_b x\]

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log3 3^2 = 2 log3 3 I am so bad at these
let's deal with log and ln today! so you can i'm really good at it!
awesome okay
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
|dw:1440780028325:dw|
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
as ln^3?
I'm sorry let me go back and try again thats wrong
okay :=)
I feel like it should be ln 3^3
yes right!
same rules apply for 2 ln x = ??
ln 2^2
hmm
there is only one `2`
oh right yeah
so just ln 2 ?
it's 2 ln of x |dw:1440780554920:dw|
oh okay
so 2 wll become exponent of x
okay
so how would yo write 2 ln x = ?
x^2 ?
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
there is plus sign which property you should apply ?
product rule?
yes right
isnt this product rule logb(x ∙ y) = logb(x) + logb(y)
so would all the logb be log3?
no simple log means log base 10
in ur question it's ln 3^3 + ln x^2
it's natural log you don't have to worry about the base
so just ln 9x^2 ? I think
yes right
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 :)))
my pleasure :=)

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