What is 2*log_{e}(e^{2x}*sin(x)) ?

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

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

simplify

2 \cdot lo g_{e} (e^{2 x} \cdot sin (x))

4 x + 2 ln (sin (x))

Solution steps

2 lo g_{e} (e^{2 x} sin (x))

Apply log rule:

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

2 lo g_{e} (e^{2 x} sin (x)) = 2 lo g_{e} (e^{2 x}) + 2 lo g_{e} (sin (x))

= 2 lo g_{e} (e^{2 x}) + 2 lo g_{e} (sin (x))

Apply log rule:

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

lo g_{e} (e^{2 x}) = 2 x lo g_{e} (e)

= 2 \cdot 2 x lo g_{e} (e) + 2 lo g_{e} (sin (x))

2 \cdot 2 x lo g_{e} (e) = 4 x

2 lo g_{e} (sin (x)) = 2 ln (sin (x))

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

ln (\frac{25 - 200}{199 - 200})

\frac{ln ( Δ x + x ) - ln ( x )}{Δ x}

(\frac{1}{54}) ln (\frac{114486}{28000})

ln (\frac{θ}{x ^{θ + 1}})

2 ln (3 t)

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