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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

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)

ln (2) \cdot \frac{1}{2}

ln ((x y)^{4})

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

2 ln (x) + ln (3)

lo g_{c} (c^{2}) - 2 lo g_{c} (c^{3})

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