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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- \frac{3}{7} \cdot lo g_{2} (\frac{3}{7}) - \frac{4}{7} \cdot lo g_{2} (\frac{4}{7})

lo g_{10} (5) + lo g_{10} (8)

\frac{1}{4} ln (y) + ln (z)

lo g_{b} (x^{5} y)

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