simplify 5ln(9/8)

Solution

simplify

5 ln (\frac{9}{8})

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

Decimal Notation

0.58891 \dots

Solution steps

5 ln (\frac{9}{8})

Apply log rule:

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

ln (\frac{9}{8}) = ln (9) - ln (8)

= 5 (ln (9) - ln (8))

ln (9) = 2 ln (3)

ln (8) = 3 ln (2)

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

2 lo g_{6} (2 x - 3) + 6 lo g_{6} (3 x + 3)

\frac{y ^{2}}{x ^{2}} + ln (\frac{x ^{6}}{y ^{2}})

\frac{ln ( 15 ) - ln ( 2 )}{ln ( 1.05 ) - ln ( 1.19 )}

\frac{ln ( 2 + \frac{( 5 i )}{( n )} ) \cdot ( 5 )}{( n )}

ln ((0.5 + \frac{0.044315}{2}) \cdot 1.05)