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Popular >

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

Solution

simplify

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

Solution

ln (x)

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

= ln (x)

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Frequently Asked Questions (FAQ)

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