simplify ln(9/5)-3

Solution

simplify

ln (\frac{9}{5}) - 3

2 ln (3) - ln (5) - 3

Decimal Notation

- 2.41221 \dots

Solution steps

ln (\frac{9}{5}) - 3

Apply log rule:

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

ln (\frac{9}{5}) = ln (9) - ln (5)

= ln (9) - ln (5) - 3

ln (9) = 2 ln (3)

= 2 ln (3) - ln (5) - 3

(0 - ln (2)) - (2 ln (2) - ln (3))

- 20 ln (\frac{33}{7})

2 ln (1 + 2)

- \frac{1}{5} ln ∣ y + 1 ∣ + \frac{1}{5} ln ∣ y - 4 ∣

- lo g_{10} (6.35 \cdot 1 0^{- 8})