What is expand log_{10}((x^3)/(5y^2)) ?

The solution to expand log_{10}((x^3)/(5y^2)) is 3log_{10}(x)-log_{10}(5)-2log_{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}((x^3)/(5y^2))

expand

lo g_{10} (\frac{x ^{3}}{5 y ^{2}})

3 lo g_{10} (x) - lo g_{10} (5) - 2 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x ^{3}}{5 y ^{2}})

Apply log rule:

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

lo g_{10} (\frac{x ^{3}}{5 y ^{2}}) = lo g_{10} (x^{3}) - lo g_{10} (5 y^{2})

= lo g_{10} (x^{3}) - lo g_{10} (5 y^{2})

Apply log rule:

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

lo g_{10} (x^{3}) = 3 lo g_{10} (x)

= 3 lo g_{10} (x) - lo g_{10} (5 y^{2})

Apply log rule:

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

lo g_{10} (5 y^{2}) = lo g_{10} (5) + lo g_{10} (y^{2})

= 3 lo g_{10} (x) - (lo g_{10} (y^{2}) + lo g_{10} (5))

Apply log rule:

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

lo g_{10} (y^{2}) = 2 lo g_{10} (y)

= 3 lo g_{10} (x) - (lo g_{10} (5) + 2 lo g_{10} (y))

- (lo g_{10} (5) + 2 lo g_{10} (y)) : - lo g_{10} (5) - 2 lo g_{10} (y)

= 3 lo g_{10} (x) - lo g_{10} (5) - 2 lo g_{10} (y)

ln 1 - 32 - ln ∣ 3 ∣

ln (\frac{( x ^{2} + 1 ) ^{5}}{( 1 - x ) ^{\frac{1}{2}}})

6 - lo g_{10} (\frac{0.035}{0.1})

- lo g_{10} (7.57 \cdot 1 0^{- 3})

\frac{1}{0.81 \cdot 1 0 ^{- 4}} ln (\frac{1.04}{0.03})

What is expand log_{10}((x^3)/(5y^2)) ?
The solution to expand log_{10}((x^3)/(5y^2)) is 3log_{10}(x)-log_{10}(5)-2log_{10}(y)