What is expand log_{e}(((2y^2))/(z^3)) ?

The solution to expand log_{e}(((2y^2))/(z^3)) is ln(2)+2ln(y)-3ln(z)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand log_{e}(((2y^2))/(z^3))

expand

lo g_{e} (\frac{( 2 y ^{2} )}{z ^{3}})

ln (2) + 2 ln (y) - 3 ln (z)

Solution steps

lo g_{e} (\frac{( 2 y ^{2} )}{z ^{3}})

Apply log rule:

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

lo g_{e} (\frac{( 2 y ^{2} )}{z ^{3}}) = lo g_{e} ((2 y^{2})) - lo g_{e} (z^{3})

= lo g_{e} (2 y^{2}) - lo g_{e} (z^{3})

Apply log rule:

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

lo g_{e} (z^{3}) = 3 lo g_{e} (z)

= lo g_{e} (2 y^{2}) - 3 lo g_{e} (z)

Apply log rule:

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

lo g_{e} (2 y^{2}) = lo g_{e} (2) + lo g_{e} (y^{2})

= lo g_{e} (2) + lo g_{e} (y^{2}) - 3 lo g_{e} (z)

Apply log rule:

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

lo g_{e} (y^{2}) = 2 lo g_{e} (y)

= lo g_{e} (2) + 2 lo g_{e} (y) - 3 lo g_{e} (z)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (2) + 2 lo g_{e} (y) - 3 lo g_{e} (z)

Simplify

lo g_{e} (y) : ln (y)

= ln (2) + 2 ln (y) - 3 lo g_{e} (z)

Simplify

lo g_{e} (z) : ln (z)

= ln (2) + 2 ln (y) - 3 ln (z)

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

ln (x - 7) + ln (x + 7)

ln (2 e^{- 6}) + (- 2.268) \cdot ln (0.15)

- ln (x + 1) + ln (x - 1) - 2 arctan (x)

lo g_{\frac{1}{2}} (\frac{1}{10})

What is expand log_{e}(((2y^2))/(z^3)) ?
The solution to expand log_{e}(((2y^2))/(z^3)) is ln(2)+2ln(y)-3ln(z)