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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

3 lo g_{4} (x) = lo g_{4} (x^{3})

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

Apply log rule:

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

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

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

ln (\frac{7}{382})

\frac{1}{5} (ln (10 + 101) - ln (- 5 + 26))

\frac{1}{2} lo g_{10} (x) - 2 lo g_{10} (y)

182000 (ln (0.58) - ln (1.3))

5 lo g_{b} (x) + 2 lo g_{b} (z)

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