What is simplify-4(1/2 ln(3)-ln(2)) ?

The solution to simplify-4(1/2 ln(3)-ln(2)) is -4ln((3^{1/2})/2)

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

simplify

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

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

Decimal Notation

0.57536 \dots

Solution steps

- 4 (\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}})

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

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

- lo g_{10} (4.24 \cdot 1 0^{(- 3)})

12 + \frac{1}{2} lo g_{10} (7) - lo g_{10} (2)

lo g_{2} (x) + 4 lo g_{2} (y)

2 (450 ln (30) - 200 - 50 ln (10))

ln (- 5 a e^{- 5 a})

What is simplify-4(1/2 ln(3)-ln(2)) ?
The solution to simplify-4(1/2 ln(3)-ln(2)) is -4ln((3^{1/2})/2)