What is ln((2^{-3})/(1125)) ?

The solution to ln((2^{-3})/(1125)) is -3ln(2)-ln(1125)

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simplify ln((2^{-3})/(1125))

simplify

ln (\frac{2 ^{- 3}}{1125})

- 3 ln (2) - ln (1125)

Decimal Notation

- 9.10497 \dots

Solution steps

ln (\frac{2 ^{- 3}}{1125})

Apply log rule:

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

ln (\frac{2 ^{- 3}}{1125}) = ln (2^{- 3}) - ln (1125)

= ln (2^{- 3}) - ln (1125)

Apply log rule:

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

ln (2^{- 3}) = - 3 ln (2)

= - 3 ln (2) - ln (1125)

ln (\frac{27}{36})

lo g_{y} (\frac{x}{4})

\frac{ln ( 2 ) - ln ( - 1 )}{9}

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

\frac{2}{3} lo g_{4} (74)

What is ln((2^{-3})/(1125)) ?
The solution to ln((2^{-3})/(1125)) is -3ln(2)-ln(1125)