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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

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

ln (a \cdot e^{(x^{2})})

3 ln (4) + ln (2^{7})

2 ln (3^{4}) + ln (3^{3}) - ln (9)

lo g_{10} ((1 - p)^{x} \cdot p)

ln (\frac{1 + x}{y})

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