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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

x x^{2} : x^{3}

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

Apply log rule:

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

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

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

ln (\frac{e ^{3 x}}{3})

12 lo g_{10} (5 x) - 6 lo g_{10} (5 y)

- 5 ln (x) - 5 ln (y)

1 - ln (6) + ln (3)

ln (\frac{15}{10})

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