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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

Popular Examples

expand log_{3}((sqrt(x^7))/(y^5))expand

lo g_{3} (\frac{x ^{7}}{y ^{5}})

simplify ln(2.8*10^{-4})+(90)/(8.314*(35+273.15))simplify

ln (2.8 \cdot 1 0^{- 4}) + \frac{90}{8.314 \cdot ( 35 + 273.15 )}

simplify 7pi(ln(7)-ln(2))simplify

7 π (ln (7) - ln (2))

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6 lo g_{b} (x) + 5 lo g_{b} (z)

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ln (\frac{3}{3 + 1})

Frequently Asked Questions (FAQ)

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