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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{2} (x) + 8 lo g_{2} (y)

- lo g_{10} (2.5 \cdot 1 0^{- 11})

\frac{1}{2} ln (4) - 4 ln (5 d)

ln (\frac{e \cdot x}{5 y ^{4}})

(0.287) ln (\frac{500}{200}) + (1.05) ln (\frac{680}{980})

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