What is ln(-1/4)-ln(-4) ?

The solution to ln(-1/4)-ln(-4) is -4ln(2)

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simplify ln(-1/4)-ln(-4)

simplify

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

- 4 ln (2)

Decimal Notation

- 2.77258 \dots

Solution steps

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

Apply log rule:

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

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

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

\frac{- \frac{1}{4}}{- 4} = \frac{1}{16}

= ln (\frac{1}{16})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (16)

Rewrite

16

in power-base form:

16 = 2^{4}

= - ln (2^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (2^{4}) = 4 ln (2)

= - 4 ln (2)

ln (9 (ln (x)))

ln (\frac{3}{2}) - ln (7) + ln (5)

4 ln (x) - ln (x y^{- 2})

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

ln (z^{2} + 3) - ln (z^{2} - 4)