What is expand log_{10}(((x^4)/y)^6) ?

The solution to expand log_{10}(((x^4)/y)^6) is 6(4log_{10}(x)-log_{10}(y))

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expand log_{10}(((x^4)/y)^6)

expand

lo g_{10} ((\frac{x ^{4}}{y})^{6})

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

Solution steps

lo g_{10} ((\frac{x ^{4}}{y})^{6})

Apply log rule:

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

lo g_{10} ((\frac{x ^{4}}{y})^{6}) = 6 lo g_{10} (\frac{x ^{4}}{y})

= 6 lo g_{10} (\frac{x ^{4}}{y})

Apply log rule:

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

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

= 6 (lo g_{10} (x^{4}) - lo g_{10} (y))

Apply log rule:

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

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

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

4 \cdot lo g_{10} (x) - (2 \cdot lo g_{10} (v) + 3 \cdot lo g_{10} (y))

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

lo g_{10} (\frac{x + 1}{x ^{2} + 1})

lo g_{10} (x^{\frac{3}{5}} y^{4})

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

What is expand log_{10}(((x^4)/y)^6) ?
The solution to expand log_{10}(((x^4)/y)^6) is 6(4log_{10}(x)-log_{10}(y))