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Popular >

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

Solution

simplify

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

Solution

k x + ln (sin (2 x))

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

k x ln (e) = k x

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

Popular Examples

simplify 86.25+10log_{10}(420/8)simplify

86.25 + 10 lo g_{10} (\frac{420}{8})

simplify ln(z^6(z+7)6(z-7)3)simplify

ln (z^{6} (z + 7) 6 (z - 7) 3)

simplify ln((6.09)/(9.42*10^{-3)})simplify

ln (\frac{6.09}{9.42 \cdot 1 0 ^{- 3}})

simplify-log_{10}(1.34*10^{-11})simplify

- lo g_{10} (1.34 \cdot 1 0^{- 11})

simplify 0.01*log_{2}(0.01)+0.99*log_{2}(0.99)simplify

0.01 \cdot lo g_{2} (0.01) + 0.99 \cdot lo g_{2} (0.99)

Frequently Asked Questions (FAQ)

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