What is 1/3 log_{8}(x+4)+7log_{8}(y) ?

The solution to 1/3 log_{8}(x+4)+7log_{8}(y) is log_{8}((x+4)^{1/3}y^7)

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simplify 1/3 log_{8}(x+4)+7log_{8}(y)

simplify

\frac{1}{3} lo g_{8} (x + 4) + 7 lo g_{8} (y)

lo g_{8} ((x + 4)^{\frac{1}{3}} y^{7})

Solution steps

\frac{1}{3} lo g_{8} (x + 4) + 7 lo g_{8} (y)

Apply log rule:

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

\frac{1}{3} lo g_{8} (x + 4) = lo g_{8} ((x + 4)^{\frac{1}{3}})

= lo g_{8} ((x + 4)^{\frac{1}{3}}) + 7 lo g_{8} (y)

Apply log rule:

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

7 lo g_{8} (y) = lo g_{8} (y^{7})

= lo g_{8} ((x + 4)^{\frac{1}{3}}) + lo g_{8} (y^{7})

Apply log rule:

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

lo g_{8} ((x + 4)^{\frac{1}{3}}) + lo g_{8} (y^{7}) = lo g_{8} (y^{7} (x + 4)^{\frac{1}{3}})

= lo g_{8} ((x + 4)^{\frac{1}{3}} y^{7})

t y (1 + ln (t y) - ln (t x))

lo g_{5} (\frac{p ^{9}}{1 1 _{q}})

ln (8) + ln (10)

ln (\frac{( r + x - 1 ) !}{x ! ( r - 1 ) !} θ^{r} (1 - θ)^{x})

ln (\frac{90}{84.37})

What is 1/3 log_{8}(x+4)+7log_{8}(y) ?
The solution to 1/3 log_{8}(x+4)+7log_{8}(y) is log_{8}((x+4)^{1/3}y^7)