What is expand log_{10}((x^2)/(y^4)) ?

The solution to expand log_{10}((x^2)/(y^4)) is 2log_{10}(x)-4log_{10}(y)

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expand log_{10}((x^2)/(y^4))

expand

lo g_{10} (\frac{x ^{2}}{y ^{4}})

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

Solution steps

lo g_{10} (\frac{x ^{2}}{y ^{4}})

Apply log rule:

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

lo g_{10} (\frac{x ^{2}}{y ^{4}}) = lo g_{10} (x^{2}) - lo g_{10} (y^{4})

= lo g_{10} (x^{2}) - lo g_{10} (y^{4})

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^{4})

Apply log rule:

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

lo g_{10} (y^{4}) = 4 lo g_{10} (y)

= 2 lo g_{10} (x) - 4 lo g_{10} (y)

lo g_{b} (x) + 2 lo g_{b} (x - 2)

2 ln (x) - \frac{1}{4} ln (y)

lo g_{b} (\frac{x ^{2} y}{z ^{9}})

lo g_{b} (2 y + 5) - \frac{1}{2} lo g_{b} (y + 3)

What is expand log_{10}((x^2)/(y^4)) ?
The solution to expand log_{10}((x^2)/(y^4)) is 2log_{10}(x)-4log_{10}(y)