What is 3ln(3)-4ln(2)+1 ?

The solution to 3ln(3)-4ln(2)+1 is ln(27/16)+1

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simplify 3ln(3)-4ln(2)+1

simplify

3 ln (3) - 4 ln (2) + 1

ln (\frac{27}{16}) + 1

Decimal Notation

1.52324 \dots

Solution steps

3 ln (3) - 4 ln (2) + 1

Apply log rule:

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

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

= ln (3^{3}) - 4 ln (2) + 1

Apply log rule:

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

4 ln (2) = ln (2^{4})

= ln (3^{3}) - ln (2^{4}) + 1

Apply log rule:

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

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

= ln (\frac{3 ^{3}}{2 ^{4}}) + 1

\frac{3 ^{3}}{2 ^{4}} = \frac{27}{16}

= ln (\frac{27}{16}) + 1

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