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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

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^{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)

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

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\frac{1}{3} ln (16 p) - 3 ln (2 p) q - 2 ln (5) p^{4} + 6 ln (q)

\frac{2}{3} ln (10)

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

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