What is 1/4 ln((3e^{3/2 x})/(3e^{3/2 x)-2}) ?

The solution to 1/4 ln((3e^{3/2 x})/(3e^{3/2 x)-2}) is 1/4 (ln(3e^{(3x)/2})-ln(3e^{(3x)/2}-2))

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simplify 1/4 ln((3e^{3/2 x})/(3e^{3/2 x)-2})

simplify

\frac{1}{4} ln (\frac{3 e ^{\frac{3}{2} x}}{3 e ^{\frac{3}{2} x} - 2})

\frac{1}{4} (ln (3 e^{\frac{3 x}{2}}) - ln (3 e^{\frac{3 x}{2}} - 2))

Solution steps

\frac{1}{4} ln (\frac{3 e ^{\frac{3}{2} x}}{3 e ^{\frac{3}{2} x} - 2})

Apply log rule:

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

ln (\frac{3 e ^{\frac{3}{2} x}}{3 e ^{\frac{3}{2} x} - 2}) = ln (3 e^{\frac{3}{2} x}) - ln (3 e^{\frac{3}{2} x} - 2)

= \frac{1}{4} (ln (3 e^{\frac{3}{2} x}) - ln (3 e^{\frac{3}{2} x} - 2))

e^{\frac{3}{2} x} = e^{\frac{3 x}{2}}

= \frac{1}{4} (ln (3 e^{\frac{3 x}{2}}) - ln (3 e^{\frac{3}{2} x} - 2))

e^{\frac{3}{2} x} = e^{\frac{3 x}{2}}

= \frac{1}{4} (ln (3 e^{\frac{3 x}{2}}) - ln (3 e^{\frac{3 x}{2}} - 2))

ln (\frac{2.3}{2.6})

\frac{1}{2} [ln (x + 1) + 2 ln (x - 1)] + 3 ln (x)

- 0.3 lo g_{2} (0.3) - 0.7 lo g_{2} (0.7)

ln (Y \cdot e^{- a (i)})

\frac{5 3 π}{6} - \frac{5 π}{4} + \frac{5 ln ( 2 )}{2}

What is 1/4 ln((3e^{3/2 x})/(3e^{3/2 x)-2}) ?
The solution to 1/4 ln((3e^{3/2 x})/(3e^{3/2 x)-2}) is 1/4 (ln(3e^{(3x)/2})-ln(3e^{(3x)/2}-2))