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Popular >

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

Solution

simplify

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

Solution

- ln (x)

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

Apply log rule:

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

= - ln (x)

Popular Examples

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lo g_{e} (\frac{115}{120})

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Frequently Asked Questions (FAQ)

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