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

The solution to ln((2sqrt(2))/2) is 1/2 ln(2)

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simplify ln((2sqrt(2))/2)

simplify

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

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

Decimal Notation

0.34657 \dots

Solution steps

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

Apply log rule:

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

ln (\frac{2 2}{2}) = ln (22) - ln (2)

= ln (22) - ln (2)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (22) = ln (2) + ln (2)

= ln (2) + ln (2) - ln (2)

Simplify

ln (2) + ln (2) - ln (2) : ln (2)

Rewrite as

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

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

ln (x) - ln (\frac{( 1 )}{1 - e ^{(- x)}})

ln (\frac{0.1}{0.05})

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

4 ln (\frac{1}{2 ^{k}}) - 4 k + 4 ln (2) k^{2} - 8 k^{2}

\frac{1}{200} ln (80)