What is ln(sqrt(n+1))-ln(sqrt(n)) ?

The solution to ln(sqrt(n+1))-ln(sqrt(n)) is ln(sqrt((n+1)/n))

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simplify ln(sqrt(n+1))-ln(sqrt(n))

simplify

ln (n + 1) - ln (n)

ln (\frac{n + 1}{n})

Solution steps

ln (n + 1) - ln (n)

Apply log rule:

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

ln (n + 1) - ln (n) = ln (\frac{n + 1}{n})

= ln (\frac{n + 1}{n})

Combine same powers :

\frac{x}{y} = \frac{x}{y}

= ln (\frac{n + 1}{n})

lo g_{2} (5) + \frac{1}{4} lo g_{2} (x)

lo g_{10} (\frac{3}{( x - y ) ^{3}})

625 ln (5) - \frac{2882}{25} - \frac{243}{5} ln (3)

ln (\frac{a x}{b y})

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

What is ln(sqrt(n+1))-ln(sqrt(n)) ?
The solution to ln(sqrt(n+1))-ln(sqrt(n)) is ln(sqrt((n+1)/n))