What is ln(x)-1/2 ln(y/x)-y/(3x) ?

The solution to ln(x)-1/2 ln(y/x)-y/(3x) is ln((xsqrt(x)sqrt(y))/y)-y/(3x)

Popular >

simplify ln(x)-1/2 ln(y/x)-y/(3x)

simplify

ln (x) - \frac{1}{2} ln (\frac{y}{x}) - \frac{y}{3 x}

ln (\frac{x x y}{y}) - \frac{y}{3 x}

Solution steps

ln (x) - \frac{1}{2} ln (\frac{y}{x}) - \frac{y}{3 x}

Apply log rule:

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

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

= ln (x) - ln ((\frac{y}{x})^{\frac{1}{2}}) - \frac{y}{3 x}

Apply log rule:

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

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

= ln \frac{x}{( \frac{y}{x} ) ^{\frac{1}{2}}} - \frac{y}{3 x}

Simplify

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

= ln (\frac{x x y}{y}) - \frac{y}{3 x}

lo g_{10} (x y)

20 lo g_{10} (\frac{4.2}{2 2})

f (x) = ln (5) + ln (7) - 3 ln^{2} (x)

2 (1 - 2 ln (1) + 3 - 2 ln (3) + 5 - 2 ln (5) + 7 - 2 ln (7))

What is ln(x)-1/2 ln(y/x)-y/(3x) ?
The solution to ln(x)-1/2 ln(y/x)-y/(3x) is ln((xsqrt(x)sqrt(y))/y)-y/(3x)