What is 2ln(x)-1/2 ln(y) ?

The solution to 2ln(x)-1/2 ln(y) is ln((x^2sqrt(y))/y)

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{2}}{y ^{\frac{1}{2}}} : \frac{x ^{2} y}{y}

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

lo g_{2} (\frac{x ^{2}}{x - 1})

lo g_{3} (7) + \frac{1}{2} lo g_{3} (t) - lo g_{3} (r)

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

lo g_{10} (\frac{100 x ^{2}}{27})

lo g_{10} (\frac{y}{10000})

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