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

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

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

simplify

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

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

Decimal Notation

0.20273 \dots

Solution steps

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

Combine same powers :

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

Rewrite as

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

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

ln (\frac{2.1 x 1 0 ^{- 4} x}{0.9025})

\frac{1}{398} ln (\frac{250}{238})

9.25 + lo g_{10} (\frac{0.18}{0.26})

- lo g_{10} (4 \cdot 1 0^{- 15})

8.314 (59 + 273) ln (0.286) - ln (1.99 \cdot 1 0^{11})

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