simplify ln(37/125)

Solution

simplify

ln (\frac{37}{125})

ln (37) - 3 ln (5)

Decimal Notation

- 1.21739 \dots

Solution steps

ln (\frac{37}{125})

Apply log rule:

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

ln (\frac{37}{125}) = ln (37) - ln (125)

= ln (37) - ln (125)

ln (125) = 3 ln (5)

= ln (37) - 3 ln (5)

lo g_{2} (\frac{x}{yz})

5 lo g_{10} (3) + 2 lo g_{10} (x)

ln (\frac{400}{369})

5 ln (x - 2) - ln (x + 2) - 3 ln (x)

ln (e^{i 0}) - ln (3 e^{i 0} + 4)