What is expand log_{10}((x^5)/(y^2)) ?

The solution to expand log_{10}((x^5)/(y^2)) is 5log_{10}(x)-2log_{10}(y)

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expand log_{10}((x^5)/(y^2))

expand

lo g_{10} (\frac{x ^{5}}{y ^{2}})

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

Solution steps

lo g_{10} (\frac{x ^{5}}{y ^{2}})

Apply log rule:

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

lo g_{10} (\frac{x ^{5}}{y ^{2}}) = lo g_{10} (x^{5}) - lo g_{10} (y^{2})

= lo g_{10} (x^{5}) - lo g_{10} (y^{2})

Apply log rule:

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

lo g_{10} (x^{5}) = 5 lo g_{10} (x)

= 5 lo g_{10} (x) - lo g_{10} (y^{2})

Apply log rule:

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

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

= 5 lo g_{10} (x) - 2 lo g_{10} (y)

lo g_{10} (x^{2} + 2 x - 15) - lo g_{10} (x^{2} - 7 x + 12)

lo g_{a} (40) + lo g_{a} (4)

lo g_{8} (x \cdot y \cdot z^{3})

ln (y \frac{y}{8 - y})

\frac{1}{2} (ln (8) x^{2} - ln (4) - 3 ln (x) - ln (y))

What is expand log_{10}((x^5)/(y^2)) ?
The solution to expand log_{10}((x^5)/(y^2)) is 5log_{10}(x)-2log_{10}(y)