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Brock Byrd

Brock Byrd

Answered question

2022-07-01

e ln ( ( 9 ) / log ( 3 ) ) = 100? Why is that?
I was messing around with my calculator and meant to put in log ( 9 ) / log ( 3 ), which was supposed to be two. I look back, and I see my mistake, but curiously, I input that to the function e ( x ) and it comes out with 100... Why is that? Why is e ln ( 9 ) / log ( 3 ) = 100?

Answer & Explanation

escampetaq5

escampetaq5

Beginner2022-07-02Added 12 answers

In the calculator log is for the decimal logarithm and ln for the natural logarithm so
ln 9 log 3 = 2 ln 3 × ln 10 ln 3 = ln 100
lilmoore11p8

lilmoore11p8

Beginner2022-07-03Added 6 answers

We can convert log ( 3 ) to base e with the change of base rule:
log ( 3 ) = ln ( 3 ) ln ( 10 )
Then the expression ( ln ( 9 ) / log ( 3 ) ) equals l n ( 9 ) ln ( 3 ) / ln ( 10 ) , which is equal to
ln ( 9 ) ln ( 10 ) ln ( 3 ) = 2 ln ( 3 ) ln ( 10 ) ln ( 3 ) = 2 ln ( 10 ) = ln ( 100 )
So e ln ( 9 ) / log ( 3 ) = e ln ( 100 ) . We know e ln ( a ) = a, so e ln ( 100 ) = 100

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