simplify ln((2x)/x)

Solution

simplify

ln (\frac{2 x}{x})

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

ln (\frac{2 x}{x})

Apply log rule:

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

ln (\frac{2 x}{x}) = ln (2 x) - ln (x)

= ln (2 x) - ln (x)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (2 x) = ln (2) + ln (x)

= ln (2) + ln (x) - ln (x)

Add similar elements:

ln (x) - ln (x) = 0

= ln (2)

lo g_{5} (\frac{125}{x + 6})

lo g_{10} (\frac{x + y}{10})

\frac{1}{3} lo g_{10} (x) - 6 lo g_{10} (sin (3 x)) + 2

ln ∣ 7 - 2 ∣ - \frac{3}{2} ln ∣ 2 \cdot 7 - 1 ∣ + 2 ln ∣ 7 + 3 ∣ + 4.83

lo g_{e} (\frac{1 0 ^{- 12}}{2})