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Popular >

simplify 2ln(e^{2x}sin(x))

Solution

simplify

2 ln (e^{2 x} sin (x))

Solution

4 x + 2 ln (sin (x))

Solution steps

2 ln (e^{2 x} sin (x))

Apply log rule:

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

2 ln (e^{2 x} sin (x)) = 2 ln (e^{2 x}) + 2 ln (sin (x))

= 2 ln (e^{2 x}) + 2 ln (sin (x))

Apply log rule:

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

ln (e^{2 x}) = 2 x ln (e)

= 2 \cdot 2 x ln (e) + 2 ln (sin (x))

2 \cdot 2 x ln (e) = 4 x

= 4 x + 2 ln (sin (x))

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Frequently Asked Questions (FAQ)

What is 2ln(e^{2x}sin(x)) ?
The solution to 2ln(e^{2x}sin(x)) is 4x+2ln(sin(x))