simplify ln((2x)/5)

Solution

simplify

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

ln (2) + ln (x) - ln (5)

Solution steps

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

Apply log rule:

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

ln (\frac{2 x}{5}) = ln (2 x) - ln (5)

= ln (2 x) - ln (5)

Apply log rule:

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

ln (2 x) = ln (2) + ln (x)

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

- \frac{5}{4} ln (\frac{0.01}{0.9})

\frac{300}{2 \cdot π \cdot 1200} \cdot ln (\frac{4 + 2 \cdot 120 0 ^{2}}{25})

\frac{- 5 ln ( 5 ) - 4 ln ( 2 )}{7 ln ( 5 ) - ln ( 2 )}

38 \cdot ln (\frac{400}{600}) - 8.314 \cdot ln (\frac{1}{10})

ln (\frac{1}{5}) - e^{(- 5^{3})}