simplify ln(8/4)

Solution

simplify

ln (\frac{8}{4})

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

ln (\frac{8}{4})

Apply log rule:

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

ln (\frac{8}{4}) = ln (8) - ln (4)

= ln (8) - ln (4)

ln (8) = 3 ln (2)

ln (4) = 2 ln (2)

= 3 ln (2) - 2 ln (2)

Add similar elements:

3 ln (2) - 2 ln (2) = ln (2)

= ln (2)

- lo g_{10} (9 \cdot 1 0^{- 3})

\frac{1}{2} lo g_{3} (x) + \frac{1}{3} lo g_{3} (2 x + 9)

2 ln (5) - 2 ln (x) - 3 ln (x^{2} - 5)

2 ln ∣ x - 2 ∣ - ln ∣ x - 3 ∣

ln (\frac{8 e ^{2 x}}{3 y ^{2}})