What is 2ln(3)-1/2 ln(2)+pi/(12) ?

The solution to 2ln(3)-1/2 ln(2)+pi/(12) is ln((9sqrt(2))/2)+pi/(12)

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simplify 2ln(3)-1/2 ln(2)+pi/(12)

simplify

2 ln (3) - \frac{1}{2} ln (2) + \frac{π}{12}

ln (\frac{9 2}{2}) + \frac{π}{12}

Decimal Notation

2.11245 \dots

Solution steps

2 ln (3) - \frac{1}{2} ln (2) + \frac{π}{12}

Apply log rule:

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

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

= ln (3^{2}) - \frac{1}{2} ln (2) + \frac{π}{12}

Apply log rule:

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

\frac{1}{2} ln (2) = ln (2^{\frac{1}{2}})

= ln (3^{2}) - ln (2^{\frac{1}{2}}) + \frac{π}{12}

Apply log rule:

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

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

= ln (\frac{3 ^{2}}{2 ^{\frac{1}{2}}}) + \frac{π}{12}

\frac{3 ^{2}}{2 ^{\frac{1}{2}}} = \frac{9 2}{2}

= ln (\frac{9 2}{2}) + \frac{π}{12}

lo g_{10} (\frac{x ^{2}}{7})

lo g_{5} (\frac{25}{x + 5})

lo g_{2} (\frac{3 y}{z})

lo g_{10} (\frac{z ^{3} x ^{4}}{y})

ln (9 x^{3})

What is 2ln(3)-1/2 ln(2)+pi/(12) ?
The solution to 2ln(3)-1/2 ln(2)+pi/(12) is ln((9sqrt(2))/2)+pi/(12)