What is ln(3-x^2)-ln(x+sqrt(3)) ?

The solution to ln(3-x^2)-ln(x+sqrt(3)) is ln(-x+sqrt(3))

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simplify ln(3-x^2)-ln(x+sqrt(3))

simplify

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

ln (- x + 3)

Solution steps

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

Apply log rule:

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

ln (3 - x^{2}) - ln (x + 3) = ln (\frac{- x ^{2} + 3}{x + 3})

= ln (\frac{3 - x ^{2}}{x + 3})

Simplify

\frac{3 - x ^{2}}{x + 3} : - x + 3

= ln (- x + 3)

ln (x^{2} - 13 x + 36) + 2 ln (x - 4) - ln (x - 9)

lo g_{b} (m^{3} n^{2} p^{5})

lo g_{8} (\frac{64}{x + 1})

lo g_{10} (\frac{x}{10 y ^{6}})

\frac{1}{3} lo g_{c} (x) + 3 lo g_{c} (y) - 5 lo g_{c} (x)

What is ln(3-x^2)-ln(x+sqrt(3)) ?
The solution to ln(3-x^2)-ln(x+sqrt(3)) is ln(-x+sqrt(3))