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

The solution to sqrt(1+ln(2)-1/2 ln(3)) is sqrt(1+ln((2\sqrt{3))/3)}

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

simplify

1 + ln (2) - \frac{1}{2} ln (3)

1 + ln (\frac{2 3}{3})

Decimal Notation

1.06950 \dots

Solution steps

1 + ln (2) - \frac{1}{2} ln (3)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

e^{l n ((c o s (x))^{- \frac{1}{2}})}

0.0259 ln (\frac{2.8 \cdot 1 0 ^{19}}{2 \cdot 1 0 ^{16}})

ln (x^{2}) + ln (y^{0.5})

ln (\frac{1}{\frac{1}{k}})

ln (\frac{15}{17})

What is sqrt(1+ln(2)-1/2 ln(3)) ?
The solution to sqrt(1+ln(2)-1/2 ln(3)) is sqrt(1+ln((2\sqrt{3))/3)}