What is y[ln(2y)-ln(1-2y)]-y[ln(y)-ln(1-y)] ?

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

Popular >

simplify y[ln(2y)-ln(1-2y)]-y[ln(y)-ln(1-y)]

simplify

y [ln (2 y) - ln (1 - 2 y)] - y [ln (y) - ln (1 - y)]

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

Solution steps

y [ln (2 y) - ln (1 - 2 y)] - y [ln (y) - ln (1 - y)]

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Remove parentheses:

(a) = a

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

ln (\frac{60}{120})

ln (- 4.2664 \cdot 1 0^{-} 6)

\frac{1}{10} ln (5000)

\frac{9}{10} ln (2 x + 4) - \frac{12}{5} ln (x + 3)

ln (- 0.21 + 6) - ln (2 (- 0.21) - 1)

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