What is 4log_{c}(8y+1)+1/5 log_{c}(y+6) ?

The solution to 4log_{c}(8y+1)+1/5 log_{c}(y+6) is log_{c}((8y+1)^4(y+6)^{1/5})

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simplify 4log_{c}(8y+1)+1/5 log_{c}(y+6)

simplify

4 lo g_{c} (8 y + 1) + \frac{1}{5} lo g_{c} (y + 6)

lo g_{c} ((8 y + 1)^{4} (y + 6)^{\frac{1}{5}})

Solution steps

4 lo g_{c} (8 y + 1) + \frac{1}{5} lo g_{c} (y + 6)

Apply log rule:

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

4 lo g_{c} (8 y + 1) = lo g_{c} ((8 y + 1)^{4})

= lo g_{c} ((8 y + 1)^{4}) + \frac{1}{5} lo g_{c} (y + 6)

Apply log rule:

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

\frac{1}{5} lo g_{c} (y + 6) = lo g_{c} ((y + 6)^{\frac{1}{5}})

= lo g_{c} ((8 y + 1)^{4}) + lo g_{c} ((y + 6)^{\frac{1}{5}})

Apply log rule:

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

lo g_{c} ((8 y + 1)^{4}) + lo g_{c} ((y + 6)^{\frac{1}{5}}) = lo g_{c} ((8 y + 1)^{4} (y + 6)^{\frac{1}{5}})

= lo g_{c} ((8 y + 1)^{4} (y + 6)^{\frac{1}{5}})

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What is 4log_{c}(8y+1)+1/5 log_{c}(y+6) ?
The solution to 4log_{c}(8y+1)+1/5 log_{c}(y+6) is log_{c}((8y+1)^4(y+6)^{1/5})