What is ln(3)+2ln(x)-ln(x+1) ?

The solution to ln(3)+2ln(x)-ln(x+1) is ln((3x^2)/(x+1))

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simplify ln(3)+2ln(x)-ln(x+1)

simplify

ln (3) + 2 ln (x) - ln (x + 1)

ln (\frac{3 x ^{2}}{x + 1})

Solution steps

ln (3) + 2 ln (x) - ln (x + 1)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (x) = ln (x^{2})

= ln (3) + ln (x^{2}) - ln (x + 1)

Apply log rule:

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

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

= ln (3 x^{2}) - ln (x + 1)

Apply log rule:

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

ln (3 x^{2}) - ln (x + 1) = ln (\frac{3 x ^{2}}{x + 1})

= ln (\frac{3 x ^{2}}{x + 1})

ln^{- 1} (ln (10) - ln (5))

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

lo g_{3} (\frac{4 x ^{2}}{y})

2 ln (2) - 2 ln (\frac{1}{2})

ln (x^{2} e^{b x})

What is ln(3)+2ln(x)-ln(x+1) ?
The solution to ln(3)+2ln(x)-ln(x+1) is ln((3x^2)/(x+1))