What is 3log_{5}(x+1)-1/2 log_{5}(w)+3 ?

The solution to 3log_{5}(x+1)-1/2 log_{5}(w)+3 is log_{5}((sqrt(w)(x+1)^3)/w)+3

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simplify 3log_{5}(x+1)-1/2 log_{5}(w)+3

simplify

3 lo g_{5} (x + 1) - \frac{1}{2} lo g_{5} (w) + 3

lo g_{5} (\frac{w ( x + 1 ) ^{3}}{w}) + 3

Solution steps

3 lo g_{5} (x + 1) - \frac{1}{2} lo g_{5} (w) + 3

Apply log rule:

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

3 lo g_{5} (x + 1) = lo g_{5} ((x + 1)^{3})

= lo g_{5} ((x + 1)^{3}) - \frac{1}{2} lo g_{5} (w) + 3

Apply log rule:

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

\frac{1}{2} lo g_{5} (w) = lo g_{5} (w^{\frac{1}{2}})

= lo g_{5} ((x + 1)^{3}) - lo g_{5} (w^{\frac{1}{2}}) + 3

Apply log rule:

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

lo g_{5} ((x + 1)^{3}) - lo g_{5} (w^{\frac{1}{2}}) = lo g_{5} (\frac{( x + 1 ) ^{3}}{w ^{\frac{1}{2}}})

= lo g_{5} (\frac{( x + 1 ) ^{3}}{w ^{\frac{1}{2}}}) + 3

Simplify

\frac{( x + 1 ) ^{3}}{w ^{\frac{1}{2}}} : \frac{w ( x + 1 ) ^{3}}{w}

= lo g_{5} (\frac{w ( x + 1 ) ^{3}}{w}) + 3

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What is 3log_{5}(x+1)-1/2 log_{5}(w)+3 ?
The solution to 3log_{5}(x+1)-1/2 log_{5}(w)+3 is log_{5}((sqrt(w)(x+1)^3)/w)+3