What is expand log_{b}((x^2y)/(z^8)) ?

The solution to expand log_{b}((x^2y)/(z^8)) is 2log_{b}(x)+log_{b}(y)-8log_{b}(z)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand log_{b}((x^2y)/(z^8))

expand

lo g_{b} (\frac{x ^{2} y}{z ^{8}})

2 lo g_{b} (x) + lo g_{b} (y) - 8 lo g_{b} (z)

Solution steps

lo g_{b} (\frac{x ^{2} y}{z ^{8}})

Apply log rule:

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

lo g_{b} (\frac{x ^{2} y}{z ^{8}}) = lo g_{b} (x^{2} y) - lo g_{b} (z^{8})

= lo g_{b} (x^{2} y) - lo g_{b} (z^{8})

Apply log rule:

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

lo g_{b} (z^{8}) = 8 lo g_{b} (z)

= lo g_{b} (x^{2} y) - 8 lo g_{b} (z)

Apply log rule:

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

lo g_{b} (x^{2} y) = lo g_{b} (x^{2}) + lo g_{b} (y)

= lo g_{b} (x^{2}) + lo g_{b} (y) - 8 lo g_{b} (z)

Apply log rule:

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

lo g_{b} (x^{2}) = 2 lo g_{b} (x)

= 2 lo g_{b} (x) + lo g_{b} (y) - 8 lo g_{b} (z)

ln (\frac{1}{2}) + ln (\frac{2}{3}) + ln (\frac{3}{5})

lo g_{3} (2 x^{2})

lo g_{3} (\frac{( x + y ) ^{2}}{x ^{2} + y ^{2}})

lo g_{4} (x^{2} - 49) - 6 lo g_{4} (x + 7)

What is expand log_{b}((x^2y)/(z^8)) ?
The solution to expand log_{b}((x^2y)/(z^8)) is 2log_{b}(x)+log_{b}(y)-8log_{b}(z)