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Bailee Short

Bailee Short

Answered question

2022-06-24

Why does the value ln ( | cos ( x ) | ) become ln ( | sec ( x ) | ) ?
I was doing an integral and I got my final answer as that, but I don't understand how you can just send the negative sign inside and make it sec ( x ) .

Answer & Explanation

klemmepk

klemmepk

Beginner2022-06-25Added 16 answers

You have
a b = c b = log a ( c ) .
Use this to show that for any power r, log b ( a r ) = r log b ( a ) for any base b.
Mohammad Cannon

Mohammad Cannon

Beginner2022-06-26Added 4 answers

Since cos x = 1 sec x , then
ln ( cos x ) = ln ( 1 sec x ) = ln 1 ( ln ( sec x ) ) = ln ( sec x )
Where we have used the basic facts that
ln 1 = 0
ln ( a b ) = ln a ln b

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