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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

\frac{\frac{1}{x + h} + 1}{\frac{1}{x} + 1} : \frac{x ( 1 + x + h )}{( x + h ) ( 1 + x )}

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

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

- 1.44 - 5 lo g_{10} (\frac{2.6}{10})

ln (4 x) + ln (x^{2})

ln (8 x^{2}) - 2 ln (2 x)

ln (x e)

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