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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{3}{8} \cdot ln (\frac{8}{3})

ln (\frac{a \cdot b}{c})

ln (0.9 x) - ln (x)

2 lo g_{3} (x) - 5 lo g_{3} (x - 3) + lo g_{3} (y)

ln (\frac{2 x}{y ^{10}})

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