What is expand log_{10}((y^4)/(x^5z)) ?

The solution to expand log_{10}((y^4)/(x^5z)) is 4log_{10}(y)-5log_{10}(x)-log_{10}(z)

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expand log_{10}((y^4)/(x^5z))

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (x^{5} z) = lo g_{10} (x^{5}) + lo g_{10} (z)

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

Apply log rule:

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

lo g_{10} (x^{5}) = 5 lo g_{10} (x)

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

- (5 lo g_{10} (x) + lo g_{10} (z)) : - 5 lo g_{10} (x) - lo g_{10} (z)

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

ln (x^{12} 5 - x)

lo g_{8} (64 x^{3})

- lo g_{10} (5.6 \cdot 1 0^{- 5})

lo g_{b} (x) + lo g_{b} (y)

lo g_{2} (\frac{5 y}{z})

What is expand log_{10}((y^4)/(x^5z)) ?
The solution to expand log_{10}((y^4)/(x^5z)) is 4log_{10}(y)-5log_{10}(x)-log_{10}(z)