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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand log_{10}(x/(y^3z))

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

2 ln (x) + 7 ln (z)

ln (\frac{e ^{8}}{11})

ln (\frac{3}{13})

ln (\frac{e ^{8}}{12})

ln (\frac{e}{( 2 π s ^{2} ) ^{\frac{1}{2}}})

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