What is (ln(6)-ln(3))*(4)-((ln(4)-ln(2))(3)) ?

The solution to (ln(6)-ln(3))*(4)-((ln(4)-ln(2))(3)) is ln(2)

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simplify (ln(6)-ln(3))*(4)-((ln(4)-ln(2))(3))

simplify

(ln (6) - ln (3)) \cdot (4) - ((ln (4) - ln (2)) (3))

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

(ln (6) - ln (3)) (4) - ((ln (4) - ln (2)) (3))

Apply log rule:

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

ln (6) - ln (3) = ln (\frac{6}{3})

= 4 ln (\frac{6}{3}) - 3 (ln (4) - ln (2))

Divide the numbers:

\frac{6}{3} = 2

= ln (2) \cdot 4 - (ln (4) - ln (2)) \cdot 3

(ln (4) - ln (2)) \cdot 3 = 3 ln (2)

= 4 ln (2) - 3 ln (2)

Add similar elements:

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

= ln (2)

20 ln (\frac{22000 e}{34 e})

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\frac{1}{2} ln (x) - \frac{3}{2} ln (\frac{1}{x})

ln (ln (x) + ln (y))

ln (0.03 t \cdot e^{- \frac{6}{100} t})

What is (ln(6)-ln(3))*(4)-((ln(4)-ln(2))(3)) ?
The solution to (ln(6)-ln(3))*(4)-((ln(4)-ln(2))(3)) is ln(2)