What is 1/2 ln(11)-1/2 ln(3) ?

The solution to 1/2 ln(11)-1/2 ln(3) is 1/2 ln(11/3)

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simplify 1/2 ln(11)-1/2 ln(3)

simplify

\frac{1}{2} ln (11) - \frac{1}{2} ln (3)

\frac{1}{2} ln (\frac{11}{3})

Decimal Notation

0.64964 \dots

Solution steps

\frac{1}{2} ln (11) - \frac{1}{2} ln (3)

Apply log rule:

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

\frac{1}{2} ln (11) = ln (1 1^{\frac{1}{2}})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Combine same powers :

= ln (\frac{11}{3})

Rewrite as

= ln ((\frac{11}{3})^{\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{11}{3})

ln (\frac{107}{100})

20 lo g_{10} (5 \cdot \frac{20}{10 \cdot 4 \cdot 30})

ln (\frac{87.41}{86})

ln (\frac{80}{12})

\frac{98 π}{3} (1 + 3 ln (3) - 6 ln (2))

What is 1/2 ln(11)-1/2 ln(3) ?
The solution to 1/2 ln(11)-1/2 ln(3) is 1/2 ln(11/3)