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

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

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expand log_{10}((x^4)/(y^3z))

expand

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

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

Solution steps

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

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

Apply log rule:

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

lo g_{10} (x^{4}) = 4 lo g_{10} (x)

= 4 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)

= 4 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)

= 4 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)

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

- ln (5) - ln (7) + ln (3)

lo g_{10} (\frac{y ^{9}}{x ^{8}})

ln (\frac{1}{3}) - e^{- (3)^{3}}

lo g_{1.8} (\frac{3.57}{3.92}) + 50.65 - 51.6

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

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