What is ln(sqrt(2))-1/2-ln(sqrt(1/6))-1/24 ?

The solution to ln(sqrt(2))-1/2-ln(sqrt(1/6))-1/24 is ln(2sqrt(3))-13/24

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simplify ln(sqrt(2))-1/2-ln(sqrt(1/6))-1/24

simplify

ln (2) - \frac{1}{2} - ln (\frac{1}{6}) - \frac{1}{24}

ln (23) - \frac{13}{24}

Decimal Notation

0.70078 \dots

Solution steps

ln (2) - \frac{1}{2} - ln (\frac{1}{6}) - \frac{1}{24}

Apply log rule:

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

ln (2) - ln (\frac{1}{6}) = ln \frac{2}{\frac{1}{6}}

= ln \frac{2}{\frac{1}{6}} - \frac{1}{2} - \frac{1}{24}

\frac{2}{\frac{1}{6}} = 23

= ln (23) - \frac{1}{2} - \frac{1}{24}

Combine the fractions

- \frac{1}{2} - \frac{1}{24} : - \frac{13}{24}

= ln (23) - \frac{13}{24}

\frac{79}{3.9} ln (\frac{32}{3})

ln ((e^{- x^{3}}) (3 x^{3}))

ln ((x^{2} + 1)^{2}) + ln ((\frac{x + 1}{x - 1})^{2})

lo g_{5} (7 \cdot 3)

7 lo g_{3} (y) - \frac{1}{4} lo g_{3} (z) + 2 lo g_{3} (x)

What is ln(sqrt(2))-1/2-ln(sqrt(1/6))-1/24 ?
The solution to ln(sqrt(2))-1/2-ln(sqrt(1/6))-1/24 is ln(2sqrt(3))-13/24