What is 1/2 ln(4sqrt(3)+8)-1/2 ln(4) ?

The solution to 1/2 ln(4sqrt(3)+8)-1/2 ln(4) is ln((sqrt(6)+sqrt(2))/2)

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simplify 1/2 ln(4sqrt(3)+8)-1/2 ln(4)

simplify

\frac{1}{2} ln (43 + 8) - \frac{1}{2} ln (4)

ln (\frac{6 + 2}{2})

Decimal Notation

0.65847 \dots

Solution steps

\frac{1}{2} ln (43 + 8) - \frac{1}{2} ln (4)

Apply log rule:

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

\frac{1}{2} ln (43 + 8) = ln ((43 + 8)^{\frac{1}{2}})

= ln ((43 + 8)^{\frac{1}{2}}) - \frac{1}{2} ln (4)

Apply log rule:

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

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

= ln ((43 + 8)^{\frac{1}{2}}) - ln (4^{\frac{1}{2}})

Apply log rule:

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

ln ((43 + 8)^{\frac{1}{2}}) - ln (4^{\frac{1}{2}}) = ln \frac{( 4 3 + 8 ) ^{\frac{1}{2}}}{4 ^{\frac{1}{2}}}

= ln \frac{( 4 3 + 8 ) ^{\frac{1}{2}}}{4 ^{\frac{1}{2}}}

\frac{( 4 3 + 8 ) ^{\frac{1}{2}}}{4 ^{\frac{1}{2}}} = \frac{6 + 2}{2}

= ln (\frac{6 + 2}{2})

\frac{7 ln ( 101 )}{2} + 534

ln (1.25 x)

ln (\frac{m !}{( 1 + x ) ^{m + 1}})

0.385 \cdot ln (\frac{333}{297})

ln (\frac{4}{648})

What is 1/2 ln(4sqrt(3)+8)-1/2 ln(4) ?
The solution to 1/2 ln(4sqrt(3)+8)-1/2 ln(4) is ln((sqrt(6)+sqrt(2))/2)