simplify ln(625/25)

Solution

simplify

ln (\frac{625}{25})

2 ln (5)

Decimal Notation

3.21887 \dots

Solution steps

ln (\frac{625}{25})

Apply log rule:

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

ln (\frac{625}{25}) = ln (625) - ln (25)

= ln (625) - ln (25)

ln (625) = 4 ln (5)

ln (25) = 2 ln (5)

= 4 ln (5) - 2 ln (5)

Add similar elements:

4 ln (5) - 2 ln (5) = 2 ln (5)

= 2 ln (5)

\frac{2}{3} (lo g_{10} (E) - lo g_{10} (0.7))

ln (\frac{- 3.95 + 8.05}{31.8})

ln (x + 2) + ln (3)

lo g_{2} (\frac{16}{x - 1})

ln (\frac{1}{21})