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Popular >

simplify 2ln(y)-ln(xy)

Solution

simplify

2 ln (y) - ln (x y)

Solution

ln (\frac{y}{x})

Solution steps

2 ln (y) - ln (x y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (y) = ln (y^{2})

= ln (y^{2}) - ln (y x)

Apply log rule:

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

ln (y^{2}) - ln (y x) = ln (\frac{y ^{2}}{y x})

= ln (\frac{y ^{2}}{x y})

Cancel the common factor:

y

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

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Frequently Asked Questions (FAQ)

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