What is ln((2sqrt(10))/5) ?

The solution to ln((2sqrt(10))/5) is ln(2)+1/2 ln(10)-ln(5)

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simplify ln((2sqrt(10))/5)

simplify

ln (\frac{2 10}{5})

ln (2) + \frac{1}{2} ln (10) - ln (5)

Solution steps

ln (\frac{2 10}{5})

Apply log rule:

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

ln (\frac{2 10}{5}) = ln (210) - ln (5)

= ln (210) - ln (5)

Apply log rule:

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

ln (210) = ln (2) + ln (10)

= ln (2) + ln (10) - ln (5)

ln (10) = \frac{1}{2} ln (10)

= ln (2) + \frac{1}{2} ln (10) - ln (5)

e^{3} ln (3 x)

ln (\frac{x - 2}{y ^{2} - x ^{2}})

ln (a P^{m})

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

\frac{ln ( 7 ) - ln ( 10 )}{5.37}

What is ln((2sqrt(10))/5) ?
The solution to ln((2sqrt(10))/5) is ln(2)+1/2 ln(10)-ln(5)