What is 3log_{m}(6w+1)+1/5 log_{m}(w+8) ?

The solution to 3log_{m}(6w+1)+1/5 log_{m}(w+8) is log_{m}((6w+1)^3(w+8)^{1/5})

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simplify 3log_{m}(6w+1)+1/5 log_{m}(w+8)

simplify

3 lo g_{m} (6 w + 1) + \frac{1}{5} lo g_{m} (w + 8)

lo g_{m} ((6 w + 1)^{3} (w + 8)^{\frac{1}{5}})

Solution steps

3 lo g_{m} (6 w + 1) + \frac{1}{5} lo g_{m} (w + 8)

Apply log rule:

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

3 lo g_{m} (6 w + 1) = lo g_{m} ((6 w + 1)^{3})

= lo g_{m} ((6 w + 1)^{3}) + \frac{1}{5} lo g_{m} (w + 8)

Apply log rule:

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

\frac{1}{5} lo g_{m} (w + 8) = lo g_{m} ((w + 8)^{\frac{1}{5}})

= lo g_{m} ((6 w + 1)^{3}) + lo g_{m} ((w + 8)^{\frac{1}{5}})

Apply log rule:

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

lo g_{m} ((6 w + 1)^{3}) + lo g_{m} ((w + 8)^{\frac{1}{5}}) = lo g_{m} ((6 w + 1)^{3} (w + 8)^{\frac{1}{5}})

= lo g_{m} ((6 w + 1)^{3} (w + 8)^{\frac{1}{5}})

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What is 3log_{m}(6w+1)+1/5 log_{m}(w+8) ?
The solution to 3log_{m}(6w+1)+1/5 log_{m}(w+8) is log_{m}((6w+1)^3(w+8)^{1/5})