What is ln((2*3)/(3*3)) ?

The solution to ln((2*3)/(3*3)) is ln(2)-ln(3)

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simplify ln((23)/(33))

simplify

ln (\frac{2 \cdot 3}{3 \cdot 3})

ln (2) - ln (3)

Decimal Notation

- 0.40546 \dots

Solution steps

ln (\frac{2 \cdot 3}{3 \cdot 3})

Apply log rule:

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

ln (\frac{2 \cdot 3}{3 \cdot 3}) = ln (2 \cdot 3) - ln (3 \cdot 3)

= ln (2 \cdot 3) - ln (3 \cdot 3)

Apply log rule:

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

ln (2 \cdot 3) = ln (2) + ln (3), ln (3 \cdot 3) = ln (3) + ln (3)

= ln (2) + ln (3) - (ln (3) + ln (3))

Add similar elements:

ln (3) + ln (3) = 2 ln (3)

= ln (2) + ln (3) - 2 ln (3)

Add similar elements:

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

= ln (2) - ln (3)

- lo g_{10} (2.1 \cdot 1 0^{- 7})

ln (\frac{0.01 - 2}{0.01})

5 ln (\frac{106}{5})

8 ln (3) - 8 ln (2)

lo g_{e} (\frac{9}{4})