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

The solution to 3+ln((3/2)^{-3})-3+ln(2^2) is ln(32/27)

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

simplify

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

ln (\frac{32}{27})

Decimal Notation

0.16989 \dots

Solution steps

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

Apply log rule:

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

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

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

(\frac{3}{2})^{- 3} \cdot 2^{2} = \frac{32}{27}

= 3 + ln (\frac{32}{27}) - 3

3 - 3 = 0

= ln (\frac{32}{27})

ln (353) - ln (277)

\frac{1}{3} lo g_{6} (x) + 2 lo g_{6} (x + 1) + 3

(\frac{17}{12})^{2} ln (\frac{17}{12})

lo g_{4} (\frac{e ^{x} + 9}{- 4})

ln (\frac{8192}{625})

What is 3+ln((3/2)^{-3})-3+ln(2^2) ?
The solution to 3+ln((3/2)^{-3})-3+ln(2^2) is ln(32/27)