What is log_{e}(1/4)+1/4 ?

The solution to log_{e}(1/4)+1/4 is 1/4-2ln(2)

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simplify log_{e}(1/4)+1/4

simplify

lo g_{e} (\frac{1}{4}) + \frac{1}{4}

\frac{1}{4} - 2 ln (2)

Decimal Notation

- 1.13629 \dots

Solution steps

lo g_{e} (\frac{1}{4}) + \frac{1}{4}

Apply log rule:

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

lo g_{e} (\frac{1}{4}) = lo g_{e} (1) - lo g_{e} (4)

= lo g_{e} (1) - lo g_{e} (4) + \frac{1}{4}

Apply log rule:

lo g_{a} (1) = 0

= 0 - lo g_{e} (4) + \frac{1}{4}

Apply log rule:

lo g_{e} (x) = ln (x)

= 0 - ln (4) + \frac{1}{4}

0 - ln (4) + \frac{1}{4} = - ln (4) + \frac{1}{4}

= \frac{1}{4} - ln (4)

ln (4) = 2 ln (2)

= \frac{1}{4} - 2 ln (2)

\frac{d}{d x} (\frac{3}{4 x}) + ln (2 x^{3})

ln (6) - ln (7) - ln (2) + ln (3)

- lo g_{10} (1.89 \cdot 1 0^{- 3})

ln (\frac{30}{42})

0.25 ln (2) + 1.75 ln (3) + 5.5 ln (2)