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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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\frac{1}{2} lo g_{7} (4 m^{2})

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