What is expand log_{10}((x^2)/(y^3)) ?

The solution to expand log_{10}((x^2)/(y^3)) is 2log_{10}(x)-3log_{10}(y)

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expand log_{10}((x^2)/(y^3))

expand

lo g_{10} (\frac{x ^{2}}{y ^{3}})

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

Solution steps

lo g_{10} (\frac{x ^{2}}{y ^{3}})

Apply log rule:

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

lo g_{10} (\frac{x ^{2}}{y ^{3}}) = lo g_{10} (x^{2}) - lo g_{10} (y^{3})

= lo g_{10} (x^{2}) - lo g_{10} (y^{3})

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^{3})

Apply log rule:

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

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

= 2 lo g_{10} (x) - 3 lo g_{10} (y)

ln (\frac{5 x ^{2}}{8 - x})

ln (\frac{27}{20})

2 ln (2) - ln 4 + x^{2}

What is expand log_{10}((x^2)/(y^3)) ?
The solution to expand log_{10}((x^2)/(y^3)) is 2log_{10}(x)-3log_{10}(y)