What is log_{3}(x)+2log_{3}(y)+1/2 log_{3}(z) ?

The solution to log_{3}(x)+2log_{3}(y)+1/2 log_{3}(z) is log_{3}(xy^2z^{1/2})

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simplify log_{3}(x)+2log_{3}(y)+1/2 log_{3}(z)

simplify

lo g_{3} (x) + 2 lo g_{3} (y) + \frac{1}{2} lo g_{3} (z)

lo g_{3} (x y^{2} z^{\frac{1}{2}})

Solution steps

lo g_{3} (x) + 2 lo g_{3} (y) + \frac{1}{2} lo g_{3} (z)

Apply log rule:

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

2 lo g_{3} (y) = lo g_{3} (y^{2})

= lo g_{3} (x) + lo g_{3} (y^{2}) + \frac{1}{2} lo g_{3} (z)

Apply log rule:

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

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

= lo g_{3} (x y^{2}) + \frac{1}{2} lo g_{3} (z)

Apply log rule:

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

\frac{1}{2} lo g_{3} (z) = lo g_{3} (z^{\frac{1}{2}})

= lo g_{3} (x y^{2}) + lo g_{3} (z^{\frac{1}{2}})

Apply log rule:

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

lo g_{3} (x y^{2}) + lo g_{3} (z^{\frac{1}{2}}) = lo g_{3} (x y^{2} z^{\frac{1}{2}})

= lo g_{3} (x y^{2} z^{\frac{1}{2}})

2 lo g_{b} (x) + 4 lo g_{b} (y) - 3 lo g_{b} (z)

ln (\frac{a ^{- 2} b ^{3}}{c ^{- 5}})

ln (x^{12} 2 - x)

2 ln (x^{3}) - 5 ln (5 y^{4})

lo g_{5} (3) - lo g_{5} (4)

What is log_{3}(x)+2log_{3}(y)+1/2 log_{3}(z) ?
The solution to log_{3}(x)+2log_{3}(y)+1/2 log_{3}(z) is log_{3}(xy^2z^{1/2})