simplify ln(81/125)

Solution

simplify

ln (\frac{81}{125})

4 ln (3) - 3 ln (5)

Decimal Notation

- 0.43386 \dots

Solution steps

ln (\frac{81}{125})

Apply log rule:

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

ln (\frac{81}{125}) = ln (81) - ln (125)

= ln (81) - ln (125)

ln (81) = 4 ln (3)

ln (125) = 3 ln (5)

= 4 ln (3) - 3 ln (5)

ln (x) - 2 ln (y)

lo g_{10} (\frac{a ^{6}}{b ^{5} c})

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

lo g_{3} (4 x^{2} y) + lo g_{3} (5 x^{3} y^{2})

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