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Popular >

simplify x-ln(e^xcos(x))

Solution

simplify

x - ln (e^{x} cos (x))

Solution

- ln (cos (x))

Solution steps

x - ln (e^{x} cos (x))

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (e^{x} cos (x)) = ln (e^{x}) + ln (cos (x))

= x - (ln (e^{x}) + ln (cos (x)))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{x}) = x ln (e)

= x - (x ln (e) + ln (cos (x)))

x ln (e) = x

= x - (x + ln (cos (x)))

- (x + ln (cos (x))) : - x - ln (cos (x))

= x - x - ln (cos (x))

Add similar elements:

x - x = 0

= - ln (cos (x))

Popular Examples

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lo g_{3} (\frac{27}{x + 7})

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lo g_{10} (\frac{b}{c}) + lo g_{10} (b c)

Frequently Asked Questions (FAQ)

What is x-ln(e^xcos(x)) ?
The solution to x-ln(e^xcos(x)) is -ln(cos(x))