What is ln((2y-1)/(y-1))-ln(2) ?

The solution to ln((2y-1)/(y-1))-ln(2) is ln((2y-1)/(2(y-1)))

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simplify ln((2y-1)/(y-1))-ln(2)

simplify

ln (\frac{2 y - 1}{y - 1}) - ln (2)

ln (\frac{2 y - 1}{2 ( y - 1 )})

Solution steps

ln (\frac{2 y - 1}{y - 1}) - ln (2)

Apply log rule:

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

ln (\frac{2 y - 1}{y - 1}) - ln (2) = ln (\frac{\frac{2 y - 1}{y - 1}}{2})

= ln (\frac{\frac{2 y - 1}{y - 1}}{2})

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{2 y - 1}{2 ( y - 1 )})

50 ln (\frac{143.33}{50}) + 14

0.5 [ln (1 - 0.68) - ln (1 + 0.68)]

ln (b \cdot e^{- c \cdot x})

lo g_{e} (3 e^{- x})

ln (4 x^{b} x^{c} x^{1 - b - c})

What is ln((2y-1)/(y-1))-ln(2) ?
The solution to ln((2y-1)/(y-1))-ln(2) is ln((2y-1)/(2(y-1)))