What is expand log_{10}((x^2)/(4y^3)) ?

The solution to expand log_{10}((x^2)/(4y^3)) is 2log_{10}(x)-2log_{10}(2)-3log_{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^2)/(4y^3))

expand

lo g_{10} (\frac{x ^{2}}{4 y ^{3}})

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

Solution steps

lo g_{10} (\frac{x ^{2}}{4 y ^{3}})

Apply log rule:

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

lo g_{10} (\frac{x ^{2}}{4 y ^{3}}) = lo g_{10} (x^{2}) - lo g_{10} (4 y^{3})

= lo g_{10} (x^{2}) - lo g_{10} (4 y^{3})

Apply log rule:

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

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

= 2 lo g_{10} (x) - lo g_{10} (4 y^{3})

Apply log rule:

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

lo g_{10} (4 y^{3}) = lo g_{10} (4) + lo g_{10} (y^{3})

= 2 lo g_{10} (x) - (lo g_{10} (y^{3}) + lo g_{10} (4))

Apply log rule:

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

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

= 2 lo g_{10} (x) - (lo g_{10} (4) + 3 lo g_{10} (y))

lo g_{10} (4) = 2 lo g_{10} (2)

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

- (2 lo g_{10} (2) + 3 lo g_{10} (y)) : - 2 lo g_{10} (2) - 3 lo g_{10} (y)

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

ln (\frac{3 \cdot x ^{4}}{y})

ln (\frac{3}{2}) - ln (2)

lo g_{3} (\frac{9 x}{y ^{2}})

20 lo g_{10} (\frac{p}{2 x 1 0 ^{- 5}})

What is expand log_{10}((x^2)/(4y^3)) ?
The solution to expand log_{10}((x^2)/(4y^3)) is 2log_{10}(x)-2log_{10}(2)-3log_{10}(y)