What is 1/3 log_{4}(x)+log_{4}(z) ?

The solution to 1/3 log_{4}(x)+log_{4}(z) is log_{4}(x^{1/3}z)

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simplify 1/3 log_{4}(x)+log_{4}(z)

simplify

\frac{1}{3} lo g_{4} (x) + lo g_{4} (z)

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

Solution steps

\frac{1}{3} lo g_{4} (x) + lo g_{4} (z)

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

- lo g_{10} (5 x 1 0^{- 4})

3 ln (x) - ln (x + 6) - ln (x - 6)

ln (\frac{R}{0.203})

5 ln (x) + 2 ln (y) + ln (z)

ln (\frac{100}{10})

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