simplify ln((2x)/y)

Solution

simplify

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

ln (2) + ln (x) - ln (y)

Solution steps

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

Apply log rule:

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

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

= ln (2 x) - ln (y)

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 (y)

ln (∣ 11.9 - 1 ∣^{2} ∣ 2 \cdot 11.9 + 1 ∣^{\frac{1}{2}})

7 lo g_{10} (y) + 2 lo g_{10} (5 y + 3)

0.7 ln (\frac{14 m}{14 x + 3 y})

- lo g_{10} (1.9 \cdot 1 0^{- 9})

ln (5.1 \cdot 1 0^{- 4}) + 0.94