What is 1/2 ln(3)+3/2 ln(2) ?

The solution to 1/2 ln(3)+3/2 ln(2) is ln(2sqrt(6))

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simplify 1/2 ln(3)+3/2 ln(2)

simplify

\frac{1}{2} ln (3) + \frac{3}{2} ln (2)

ln (26)

Decimal Notation

1.58902 \dots

Solution steps

\frac{1}{2} ln (3) + \frac{3}{2} ln (2)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{\frac{1}{2}} \cdot 2^{\frac{3}{2}} = 26

= ln (26)

ln (\frac{x}{x - 1}) + ln (\frac{x + 1}{x})

ln (\frac{3}{22})

\frac{- ( \frac{y}{x} ) ^{2}}{2} + \frac{8}{7} \frac{y}{x} - \frac{3}{7} ln (\frac{y}{x})

8.07428 ln \frac{P}{( P - 90 )} - 8.07428 ln (\frac{4}{41})

- lo g_{10} (3.98 \cdot 1 0^{- 7})

What is 1/2 ln(3)+3/2 ln(2) ?
The solution to 1/2 ln(3)+3/2 ln(2) is ln(2sqrt(6))