What is expand log_{10}((x^2)/(y^5)) ?

The solution to expand log_{10}((x^2)/(y^5)) is 2log_{10}(x)-5log_{10}(y)

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expand log_{10}((x^2)/(y^5))

expand

lo g_{10} (\frac{x ^{2}}{y ^{5}})

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

Solution steps

lo g_{10} (\frac{x ^{2}}{y ^{5}})

Apply log rule:

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

lo g_{10} (\frac{x ^{2}}{y ^{5}}) = lo g_{10} (x^{2}) - lo g_{10} (y^{5})

= lo g_{10} (x^{2}) - lo g_{10} (y^{5})

Apply log rule:

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

lo g_{10} (x^{2}) = 2 lo g_{10} (x)

= 2 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)

= 2 lo g_{10} (x) - 5 lo g_{10} (y)

(lo g_{c} (x) - lo g_{c} (y)) + 7 lo g_{c} (v)

10 lo g_{6} (x) - 2 lo g_{6} (y)

lo g_{10} (23 pq)

lo g_{b} (\frac{32}{125})

- 5 ln (x) - 9 ln (y) + \frac{1}{9} ln (z)

What is expand log_{10}((x^2)/(y^5)) ?
The solution to expand log_{10}((x^2)/(y^5)) is 2log_{10}(x)-5log_{10}(y)