What is 2(log_{6}(x)+log_{6}(y^2))-log_{6}(x+2) ?

The solution to 2(log_{6}(x)+log_{6}(y^2))-log_{6}(x+2) is log_{6}((x^2y^4)/(x+2))

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simplify 2(log_{6}(x)+log_{6}(y^2))-log_{6}(x+2)

simplify

2 (lo g_{6} (x) + lo g_{6} (y^{2})) - lo g_{6} (x + 2)

lo g_{6} (\frac{x ^{2} y ^{4}}{x + 2})

Solution steps

2 (lo g_{6} (x) + lo g_{6} (y^{2})) - lo g_{6} (x + 2)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{6} (x) + lo g_{6} (y^{2}) = lo g_{6} (x y^{2})

= 2 lo g_{6} (x y^{2}) - lo g_{6} (x + 2)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

2 lo g_{6} (x y^{2}) = lo g_{6} ((x y^{2})^{2})

= lo g_{6} ((x y^{2})^{2}) - lo g_{6} (x + 2)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{6} ((x y^{2})^{2}) - lo g_{6} (x + 2) = lo g_{6} (\frac{( x y ^{2} ) ^{2}}{x + 2})

= lo g_{6} (\frac{( x y ^{2} ) ^{2}}{x + 2})

Simplify

(x y^{2})^{2} : x^{2} y^{4}

= lo g_{6} (\frac{x ^{2} y ^{4}}{x + 2})

lo g_{2} (m) + \frac{1}{2} lo g_{2} (n) + 4

lo g_{7} (6) - lo g_{7} (x)

ln (\frac{39}{52})

ln (\frac{( \frac{5.5}{12} )}{10})

What is 2(log_{6}(x)+log_{6}(y^2))-log_{6}(x+2) ?
The solution to 2(log_{6}(x)+log_{6}(y^2))-log_{6}(x+2) is log_{6}((x^2y^4)/(x+2))