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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{5} ((x - 1)^{2}) - lo g_{5} (x^{2} - 3)

lo g_{e} (\frac{1}{x})

- lo g_{10} (6.5 \times 1 0^{- 5})

ln (\frac{( x ^{2} - 1 ) ^{3}}{( x + 3 ) ^{2}})

lo g_{10} (x) - 4 lo g_{10} (y) + 5 lo g_{10} (z)

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