What is ln(6+x^2)+2ln(x)-ln(x+1) ?

The solution to ln(6+x^2)+2ln(x)-ln(x+1) is ln(((6+x^2)x^2)/(x+1))

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simplify ln(6+x^2)+2ln(x)-ln(x+1)

simplify

ln (6 + x^{2}) + 2 ln (x) - ln (x + 1)

ln (\frac{( 6 + x ^{2} ) x ^{2}}{x + 1})

Solution steps

ln (6 + x^{2}) + 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 (x^{2} + 6) + ln (x^{2}) - ln (x + 1)

Apply log rule:

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

ln (6 + x^{2}) + ln (x^{2}) = ln (x^{2} (x^{2} + 6))

= ln ((6 + x^{2}) x^{2}) - ln (x + 1)

Apply log rule:

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

ln (x^{2} (6 + x^{2})) - ln (x + 1) = ln (\frac{x ^{2} ( x ^{2} + 6 )}{x + 1})

= ln (\frac{( 6 + x ^{2} ) x ^{2}}{x + 1})

16 ln (5) - 4 ln (2)

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

ln (\frac{0.49}{0.945})

ln (t^{x i} (1 - t)^{1 - x i})

lo g_{2} (\frac{y}{z})

What is ln(6+x^2)+2ln(x)-ln(x+1) ?
The solution to ln(6+x^2)+2ln(x)-ln(x+1) is ln(((6+x^2)x^2)/(x+1))