What is expand log_{10}((x^3)/(y^5)) ?

The solution to expand log_{10}((x^3)/(y^5)) is 3log_{10}(x)-5log_{10}(y)

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expand log_{10}((x^3)/(y^5))

expand

lo g_{10} (\frac{x ^{3}}{y ^{5}})

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

Solution steps

lo g_{10} (\frac{x ^{3}}{y ^{5}})

Apply log rule:

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

lo g_{10} (\frac{x ^{3}}{y ^{5}}) = lo g_{10} (x^{3}) - lo g_{10} (y^{5})

= lo g_{10} (x^{3}) - lo g_{10} (y^{5})

Apply log rule:

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

lo g_{10} (x^{3}) = 3 lo g_{10} (x)

= 3 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)

= 3 lo g_{10} (x) - 5 lo g_{10} (y)

lo g_{2} (11) - lo g_{2} (9)

lo g_{2} ((\frac{5}{4})^{x - 3})

lo g_{5} (\frac{a ^{2} b ^{2} x}{c ^{3}})

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

ln (y e^{x})

What is expand log_{10}((x^3)/(y^5)) ?
The solution to expand log_{10}((x^3)/(y^5)) is 3log_{10}(x)-5log_{10}(y)