What is ln((8x-2)/(sqrt(x+2))sin(e^x)) ?

The solution to ln((8x-2)/(sqrt(x+2))sin(e^x)) is ln(8x-2)-ln(sqrt(x+2))+ln(sin(e^x))

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simplify ln((8x-2)/(sqrt(x+2))sin(e^x))

simplify

ln (\frac{8 x - 2}{x + 2} sin (e^{x}))

ln (8 x - 2) - ln (x + 2) + ln (sin (e^{x}))

Solution steps

ln (\frac{8 x - 2}{x + 2} sin (e^{x}))

Apply log rule:

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

ln (\frac{8 x - 2}{x + 2} sin (e^{x})) = ln (\frac{8 x - 2}{x + 2}) + ln (sin (e^{x}))

= ln (\frac{8 x - 2}{x + 2}) + ln (sin (e^{x}))

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{8 x - 2}{x + 2}) = ln (8 x - 2) - ln (x + 2)

= ln (8 x - 2) - ln (x + 2) + ln (sin (e^{x}))

- \frac{1}{0.05} ln (\frac{0.6}{8})

\frac{2}{9} ln (3)

ln (\frac{x ^{2}}{y ^{5}})

lo g_{e} (4) - lo g_{e} (2) - lo g_{e} (3)

ln (13) - ln (12)

What is ln((8x-2)/(sqrt(x+2))sin(e^x)) ?
The solution to ln((8x-2)/(sqrt(x+2))sin(e^x)) is ln(8x-2)-ln(sqrt(x+2))+ln(sin(e^x))