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Popular >

simplify ln(e^xsin(2x))

Solution

simplify

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

Solution

x + ln (sin (2 x))

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

x ln (e) = x

= x + ln (sin (2 x))

Popular Examples

join (ln(A/b))/(2ln(10))join

\frac{ln ( \frac{A}{b} )}{2 ln ( 10 )}

simplify 1/2 ln(2x+5)-1/3 ln(x+8)+ln(C)simplify

\frac{1}{2} ln (2 x + 5) - \frac{1}{3} ln (x + 8) + ln (C)

simplify-log_{10}(7.83*10^{-8})simplify

- lo g_{10} (7.83 \cdot 1 0^{- 8})

simplify ln(8*12)simplify

ln (8 \cdot 12)

simplify ln(((75+x))/(75))simplify

ln (\frac{( 75 + x )}{75})

Frequently Asked Questions (FAQ)

What is ln(e^xsin(2x)) ?
The solution to ln(e^xsin(2x)) is x+ln(sin(2x))