simplify ln(1/49)

Solution

simplify

ln (\frac{1}{49})

- 2 ln (7)

Decimal Notation

- 3.89182 \dots

Solution steps

ln (\frac{1}{49})

Apply log rule:

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

ln (\frac{1}{49}) = ln (1) - ln (49)

= ln (1) - ln (49)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (49)

0 - ln (49) = - ln (49)

= - ln (49)

Simplify

ln (49) : 2 ln (7)

= - 2 ln (7)

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

ln (\frac{20}{30})

- lo g_{10} (3 \cdot 1 0^{- 7})