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Popular >

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

Solution

simplify

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

Solution

- ln (2)

+1

Decimal Notation

- 0.69314 \dots

Solution steps

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

Apply log rule:

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

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

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

\frac{\frac{1}{x}}{\frac{2}{x}} = \frac{1}{2}

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

Apply log rule:

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

= - ln (2)

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Frequently Asked Questions (FAQ)

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