What is 8/6*ln((13*15*17*19*21*23)/(12^6)) ?

The solution to 8/6*ln((13*15*17*19*21*23)/(12^6)) is (4(ln(30421755)-6ln(12)))/3

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simplify 8/6ln((131517192123)/(12^6))

simplify

\frac{8}{6} \cdot ln (\frac{13 \cdot 15 \cdot 17 \cdot 19 \cdot 21 \cdot 23}{1 2 ^{6}})

\frac{4 ( ln ( 30421755 ) - 6 ln ( 12 ) )}{3}

Decimal Notation

3.09497 \dots

Solution steps

\frac{8}{6} ln (\frac{13 \cdot 15 \cdot 17 \cdot 19 \cdot 21 \cdot 23}{1 2 ^{6}})

Apply log rule:

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

ln (\frac{13 \cdot 15 \cdot 17 \cdot 19 \cdot 21 \cdot 23}{1 2 ^{6}}) = ln (13 \cdot 15 \cdot 17 \cdot 19 \cdot 21 \cdot 23) - ln (1 2^{6})

= \frac{8}{6} (ln (13 \cdot 15 \cdot 17 \cdot 19 \cdot 21 \cdot 23) - ln (1 2^{6}))

Apply log rule:

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

ln (1 2^{6}) = 6 ln (12)

= \frac{8}{6} (ln (13 \cdot 15 \cdot 17 \cdot 19 \cdot 21 \cdot 23) - 6 ln (12))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{8 ( ln ( 13 \cdot 15 \cdot 17 \cdot 19 \cdot 21 \cdot 23 ) - 6 ln ( 12 ) )}{6}

Multiply the numbers:

13 \cdot 15 \cdot 17 \cdot 19 \cdot 21 \cdot 23 = 30421755

= \frac{8 ( ln ( 30421755 ) - 6 ln ( 12 ) )}{6}

Cancel the common factor:

2

= \frac{4 ( ln ( 30421755 ) - 6 ln ( 12 ) )}{3}

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What is 8/6*ln((13*15*17*19*21*23)/(12^6)) ?
The solution to 8/6*ln((13*15*17*19*21*23)/(12^6)) is (4(ln(30421755)-6ln(12)))/3