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

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

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

simplify

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

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

Solution steps

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

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

3 ln ∣ x + 2 ∣ + 2 ln ∣ x - 2 ∣

8.314 \cdot 298 \cdot (ln (0.03 3^{5}) - ln (0.74 9^{5}))

ln (\frac{1}{4 x - 10})

ln (\frac{3.64}{23}) + \frac{2 \cdot 2}{23}

(4186) ln (0.77090493) - 8.314 ln (0.1)

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