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

The solution to ln(1/(x(2x-1))) is -(ln(x)+ln(2x-1))

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

simplify

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

- (ln (x) + ln (2 x - 1))

Solution steps

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

Apply log rule:

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

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

= ln (1) - ln (x (2 x - 1))

Apply log rule:

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

ln (x (2 x - 1)) = ln (x) + ln (2 x - 1)

= ln (1) - (ln (x) + ln (2 x - 1))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (ln (x) + ln (2 x - 1))

0 - (ln (x) + ln (2 x - 1)) = - (ln (x) + ln (2 x - 1))

= - (ln (x) + ln (2 x - 1))

ln (\frac{0.003789035}{0.001129995})

ln (\frac{6}{16})

ln (\frac{e ^{x + 2 y}}{1 - ( e ^{x + 2 y} )})

- lo g_{10} (\frac{1 0 ^{- 14}}{2 \cdot 1 0 ^{- 9}})