What is 1/3 log_{10}(x)-4log_{10}(y) ?

The solution to 1/3 log_{10}(x)-4log_{10}(y) is log_{10}((x^{1/3})/(y^4))

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simplify 1/3 log_{10}(x)-4log_{10}(y)

simplify

\frac{1}{3} lo g_{10} (x) - 4 lo g_{10} (y)

lo g_{10} (\frac{x ^{\frac{1}{3}}}{y ^{4}})

Solution steps

\frac{1}{3} lo g_{10} (x) - 4 lo g_{10} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{3} lo g_{10} (x) = lo g_{10} (x^{\frac{1}{3}})

= lo g_{10} (x^{\frac{1}{3}}) - 4 lo g_{10} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{10} (x^{\frac{1}{3}}) - lo g_{10} (y^{4})

Apply log rule:

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

lo g_{10} (x^{\frac{1}{3}}) - lo g_{10} (y^{4}) = lo g_{10} (\frac{x ^{\frac{1}{3}}}{y ^{4}})

= lo g_{10} (\frac{x ^{\frac{1}{3}}}{y ^{4}})

lo g_{4} (16 x^{8})

ln (\frac{1}{12})

ln (\frac{x ^{2} + 1}{x ^{2} - 1})

\frac{1}{3} lo g_{2} (3) + \frac{2}{3} lo g_{2} (\frac{3}{2})

lo g_{2} ((r + s) \cdot t)

What is 1/3 log_{10}(x)-4log_{10}(y) ?
The solution to 1/3 log_{10}(x)-4log_{10}(y) is log_{10}((x^{1/3})/(y^4))