What is ln((xsqrt(x)y)/(y^2)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((xsqrt(x)y)/(y^2))

simplify

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

ln (x) + ln (x) - ln (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= ln (x x y) - 2 ln (y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (x x y) = ln (x) + ln (x) + ln (y)

= ln (x) + ln (x) + ln (y) - 2 ln (y)

Add similar elements:

ln (y) - 2 ln (y) = - ln (y)

= ln (x) + ln (x) - ln (y)

ln (\frac{6.61}{0.36})

ln (\frac{5 x ^{4}}{cos ( x )})

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

ln (\frac{7.33}{1.67})

ln (16 y^{2})

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