What is expand log_{10}((x^3)/(y^4)) ?

The solution to expand log_{10}((x^3)/(y^4)) is 3log_{10}(x)-4log_{10}(y)

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expand log_{10}((x^3)/(y^4))

expand

lo g_{10} (\frac{x ^{3}}{y ^{4}})

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

Solution steps

lo g_{10} (\frac{x ^{3}}{y ^{4}})

Apply log rule:

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

lo g_{10} (\frac{x ^{3}}{y ^{4}}) = lo g_{10} (x^{3}) - lo g_{10} (y^{4})

= lo g_{10} (x^{3}) - lo g_{10} (y^{4})

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^{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)

= 3 lo g_{10} (x) - 4 lo g_{10} (y)

2 lo g_{10} (b x) + 3 lo g_{10} (b) y

lo g_{3} (x) - lo g_{3} (x^{6})

lo g_{4} (6 x) - lo g_{4} (10)

5 lo g_{b} (x^{2}) + lo g_{b} (x)

lo g_{4} (9^{3})

What is expand log_{10}((x^3)/(y^4)) ?
The solution to expand log_{10}((x^3)/(y^4)) is 3log_{10}(x)-4log_{10}(y)