simplify ln(e/4)

Solution

simplify

ln (\frac{e}{4})

1 - 2 ln (2)

Decimal Notation

- 0.38629 \dots

Solution steps

ln (\frac{e}{4})

Apply log rule:

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

ln (\frac{e}{4}) = ln (e) - ln (4)

= ln (e) - ln (4)

Apply log rule:

lo g_{a} (a) = 1

= 1 - ln (4)

ln (4) = 2 ln (2)

= 1 - 2 ln (2)

lo g_{m} (m x^{2})

ln (2) + x ln (x) + x - 2 ln (x - 1) - 3

ln (\frac{x ^{2} x ^{2} + 7}{( x + 7 ) ^{9}})

lo g_{10} (\frac{x ^{4} y}{z})

lo g_{7} (4 yz)