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

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

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

simplify

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

- ln (2 + x)

Solution steps

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

Apply log rule:

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

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

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

Simplify

\frac{\frac{1 + x}{2 + x}}{x + 1} : \frac{1}{2 + x}

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

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (x + 2)

ln (\frac{U ^{\frac{3}{2}} V}{N ^{\frac{5}{2}}})

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ln (- 1) - ln (3)

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