What is ln(2)+2ln(3)-ln(3)-2ln(2) ?

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

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simplify ln(2)+2ln(3)-ln(3)-2ln(2)

simplify

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

ln (\frac{3}{2})

Decimal Notation

0.40546 \dots

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

ln (2) + ln (3^{2}) = ln (3^{2} \cdot 2)

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

2 \cdot 3^{2} = 18

= ln (18) - ln (3) - 2 ln (2)

Apply log rule:

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

ln (18) - ln (3) = ln (\frac{18}{3})

= ln (\frac{18}{3}) - 2 ln (2)

Divide the numbers:

\frac{18}{3} = 6

= ln (6) - 2 ln (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (6) - ln (2^{2})

Apply log rule:

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

ln (6) - ln (2^{2}) = ln (\frac{6}{2 ^{2}})

= ln (\frac{6}{2 ^{2}})

\frac{6}{2 ^{2}} = \frac{3}{2}

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

ln (5) + 4 ln (2)

ln (x - 1) - ln (x - 2)

lo g_{e} (\frac{19}{20})

ln (3) - ln (6) - ln (5)

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

What is ln(2)+2ln(3)-ln(3)-2ln(2) ?
The solution to ln(2)+2ln(3)-ln(3)-2ln(2) is ln(3/2)