What is expand log_{10}(sqrt(x^9y^{-10)}) ?

The solution to expand log_{10}(sqrt(x^9y^{-10)}) is 9/2 log_{10}(x)-5log_{10}(y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand log_{10}(sqrt(x^9y^{-10)})

expand

lo g_{10} (x^{9} y^{- 10})

\frac{9}{2} lo g_{10} (x) - 5 lo g_{10} (y)

Solution steps

lo g_{10} (x^{9} y^{- 10})

x^{9} y^{- 10} = \frac{x ^{4} x}{y ^{5}}

= lo g_{10} (\frac{x ^{4} x}{y ^{5}})

Apply log rule:

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

lo g_{10} (\frac{x ^{4} x}{y ^{5}}) = lo g_{10} (x^{4} x) - lo g_{10} (y^{5})

= lo g_{10} (x^{4} x) - lo g_{10} (y^{5})

Simplify

lo g_{10} (y^{5}) : 5 lo g_{10} (y)

lo g_{10} (x^{4} x) = \frac{9}{2} lo g_{10} (x)

= \frac{9}{2} lo g_{10} (x) - 5 lo g_{10} (y)

(π - 15)^{2}

\frac{1}{2} (3 (- 2, 3) + (- 3, - 2))

(x + y)^{8}

(3 x - 3)^{2}

(w - \frac{5}{7}) (w + \frac{5}{7})

What is expand log_{10}(sqrt(x^9y^{-10)}) ?
The solution to expand log_{10}(sqrt(x^9y^{-10)}) is 9/2 log_{10}(x)-5log_{10}(y)