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

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

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

simplify

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

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

Decimal Notation

0.32696 \dots

Solution steps

\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}})

= 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}})

= 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}}})

= 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}

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

ln (- 6 \cdot \frac{e ^{2.11367}}{3})

lo g_{5} ((x^{2} y)^{6})

7 lo g_{3} (x) + 4 lo g_{3} (z) - 6 lo g_{3} (y)

lo g_{10} (\frac{1}{e ^{x}})

ln (\frac{270.5}{250}) (0.2872)

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