simplify ln(1/40)

Solution

simplify

ln (\frac{1}{40})

- ln (40)

Decimal Notation

- 3.68887 \dots

Solution steps

ln (\frac{1}{40})

Apply log rule:

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

ln (\frac{1}{40}) = ln (1) - ln (40)

= ln (1) - ln (40)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (40)

0 - ln (40) = - ln (40)

= - ln (40)

ln (\frac{23138}{1500})

2 (ln (\frac{x - 25}{25} + 1) - ln (\frac{x - 25}{25} - 1))

ln (40) - ln (400)

ln (\frac{x - 1}{x}) + c

2 + 3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (x + 7)