What is 3log_{b}(m+2)+1/2 log_{b}(m) ?

The solution to 3log_{b}(m+2)+1/2 log_{b}(m) is log_{b}((m+2)^3m^{1/2})

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simplify 3log_{b}(m+2)+1/2 log_{b}(m)

simplify

3 lo g_{b} (m + 2) + \frac{1}{2} lo g_{b} (m)

lo g_{b} ((m + 2)^{3} m^{\frac{1}{2}})

Solution steps

3 lo g_{b} (m + 2) + \frac{1}{2} lo g_{b} (m)

Apply log rule:

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

3 lo g_{b} (m + 2) = lo g_{b} ((m + 2)^{3})

= lo g_{b} ((m + 2)^{3}) + \frac{1}{2} lo g_{b} (m)

Apply log rule:

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

\frac{1}{2} lo g_{b} (m) = lo g_{b} (m^{\frac{1}{2}})

= lo g_{b} ((m + 2)^{3}) + lo g_{b} (m^{\frac{1}{2}})

Apply log rule:

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

lo g_{b} ((m + 2)^{3}) + lo g_{b} (m^{\frac{1}{2}}) = lo g_{b} (m^{\frac{1}{2}} (m + 2)^{3})

= lo g_{b} ((m + 2)^{3} m^{\frac{1}{2}})

ln (7 e)

\frac{1}{2} (lo g_{2} (x) + lo g_{2} (y))

lo g_{3} (x^{2}) + lo g_{3} (y^{3}) - lo g_{3} (z)

ln (\frac{53}{2})

ln (9 y)

What is 3log_{b}(m+2)+1/2 log_{b}(m) ?
The solution to 3log_{b}(m+2)+1/2 log_{b}(m) is log_{b}((m+2)^3m^{1/2})