What is ln(sqrt(2u))-ln(sqrt(u/2)) ?

The solution to ln(sqrt(2u))-ln(sqrt(u/2)) is ln(2)

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simplify ln(sqrt(2u))-ln(sqrt(u/2))

simplify

ln (2 u) - ln (\frac{u}{2})

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

ln (2 u) - ln (\frac{u}{2})

Apply log rule:

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

ln (2 u) - ln (\frac{u}{2}) = ln (\frac{2 u}{\frac{u}{2}})

= ln (\frac{2 u}{\frac{u}{2}})

\frac{2 u}{\frac{u}{2}} = 2

= ln (2)

lo g_{a} (3 x yz)

14 + lo g_{10} (1.8 \cdot 1 0^{- 5})

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

lo g_{10} (\frac{x ^{13} y ^{19}}{z ^{13}})

ln (\frac{( 3 ^{x} 6 ^{3 x} )}{2 ^{3 x}})

What is ln(sqrt(2u))-ln(sqrt(u/2)) ?
The solution to ln(sqrt(2u))-ln(sqrt(u/2)) is ln(2)