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

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

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

simplify

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

ln (23)

Decimal Notation

1.24245 \dots

Solution steps

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

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

Apply log rule:

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

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

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

Combine same powers :

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

Apply log rule:

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

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

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

\frac{3}{2} \cdot 2^{\frac{3}{2}} = 23

= ln (23)

50 \cdot ln (\frac{72}{54.8})

- lo g_{10} (6.21 x 1 0^{- 5})

\frac{1925.3}{ln ( 2 )} \cdot ln (\frac{1801}{627})

lo g_{10} (\frac{1}{5.25 \cdot 1 0 ^{- 8}})

2500 - (ln (x^{2} + 6 x + 9) - ln (x + 3))

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