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

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

Popular >

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

simplify

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

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

Decimal Notation

0.28768 \dots

Solution steps

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

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

Apply log rule:

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

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

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

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

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

Remove parentheses:

(a) = a

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

- \frac{ln ( 20 )}{9 ln ( 10 )}

ln (\frac{( 2 )}{0.273})

8 lo g_{5} (u) + 2 lo g_{5} (v)

ln (\frac{6 x - 1}{2 x ^{3} + 4 x})

6 ln (\frac{6}{5})

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