What is 8*(1/2 ln(25)-1/2 ln(13)) ?

The solution to 8*(1/2 ln(25)-1/2 ln(13)) is 8ln((5sqrt(13))/(13))

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simplify 8*(1/2 ln(25)-1/2 ln(13))

simplify

8 \cdot (\frac{1}{2} ln (25) - \frac{1}{2} ln (13))

8 ln (\frac{5 13}{13})

Decimal Notation

2.61570 \dots

Solution steps

8 (\frac{1}{2} ln (25) - \frac{1}{2} ln (13))

Apply log rule:

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

\frac{1}{2} ln (25) = ln (2 5^{\frac{1}{2}})

= 8 (ln (2 5^{\frac{1}{2}}) - \frac{1}{2} ln (13))

Apply log rule:

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

\frac{1}{2} ln (13) = ln (1 3^{\frac{1}{2}})

= 8 (ln (2 5^{\frac{1}{2}}) - ln (1 3^{\frac{1}{2}}))

Apply log rule:

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

ln (2 5^{\frac{1}{2}}) - ln (1 3^{\frac{1}{2}}) = ln (\frac{2 5 ^{\frac{1}{2}}}{1 3 ^{\frac{1}{2}}})

= 8 ln (\frac{2 5 ^{\frac{1}{2}}}{1 3 ^{\frac{1}{2}}})

\frac{2 5 ^{\frac{1}{2}}}{1 3 ^{\frac{1}{2}}} = \frac{5 13}{13}

= 8 ln (\frac{5 13}{13})

ln (\frac{( 16 + x ^{2} + x )}{4})

\frac{ln ( 1155.685 ) - ln ( 1094.66 )}{2}

2000 ln (\frac{3}{2})

\frac{5 ln ( 5 )}{4 ln ( 3 ) - 2 ln ( 5 )}

- 0.287 \cdot ln (\frac{100}{1000})

What is 8*(1/2 ln(25)-1/2 ln(13)) ?
The solution to 8*(1/2 ln(25)-1/2 ln(13)) is 8ln((5sqrt(13))/(13))