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

- anonymous

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

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- Nnesha

same like log :=)

- Nnesha

power rule first
:=) it's like backwards :=)

- Nnesha

power rule \[\large\rm log_b x^y = y \log_b x\]

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## More answers

- anonymous

log3 3^2 = 2 log3 3 I am so bad at these

- Nnesha

let's deal with log and ln today!
so you can i'm really good at it!

- anonymous

awesome okay

- 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

|dw:1440780028325:dw|

- 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

as ln^3?

- anonymous

I'm sorry let me go back and try again thats wrong

- Nnesha

okay :=)

- anonymous

I feel like it should be ln 3^3

- Nnesha

yes right!

- Nnesha

same rules apply for 2 ln x = ??

- anonymous

ln 2^2

- Nnesha

hmm

- Nnesha

there is only one `2`

- anonymous

oh right yeah

- anonymous

so just ln 2 ?

- Nnesha

it's 2 ln of x |dw:1440780554920:dw|

- anonymous

oh okay

- Nnesha

so 2 wll become exponent of x

- anonymous

okay

- Nnesha

so how would yo write 2 ln x = ?

- anonymous

x^2 ?

- 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

there is plus sign which property you should apply ?

- anonymous

product rule?

- Nnesha

yes right

- anonymous

isnt this product rule
logb(x ∙ y) = logb(x) + logb(y)

- anonymous

so would all the logb be log3?

- Nnesha

no simple log means log base 10

- Nnesha

in ur question it's ln 3^3 + ln x^2

- Nnesha

it's natural log you don't have to worry about the base

- anonymous

so just ln 9x^2 ? I think

- Nnesha

yes right

- 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

my pleasure :=)

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