simplify 25ln(25/8)

Solution

simplify

25 ln (\frac{25}{8})

25 (2 ln (5) - 3 ln (2))

Decimal Notation

28.48585 \dots

Solution steps

25 ln (\frac{25}{8})

Apply log rule:

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

ln (\frac{25}{8}) = ln (25) - ln (8)

= 25 (ln (25) - ln (8))

ln (25) = 2 ln (5)

ln (8) = 3 ln (2)

= 25 (2 ln (5) - 3 ln (2))

10 lo g_{10} (\frac{1}{1 + ( 2 π \cdot 400 \cdot 5.03 \cdot 9.566 ) ^{2}})

\frac{ln ( \frac{162}{5} )}{3 ln ( 3 )}

2 \cdot ln (\frac{1}{6})

\frac{( ln ( 20 ) + ln ( 25 ) )}{3 ln ( 5 )}

\frac{1}{2} ln (9 x^{2}) + 2 ln (x) - 3 ln (2 x)