What is log_{6}((8x^2)/((x+2))) ?

The solution to log_{6}((8x^2)/((x+2))) is 3log_{6}(2)+2log_{6}(x)-log_{6}(x+2)

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simplify log_{6}((8x^2)/((x+2)))

simplify

lo g_{6} (\frac{8 x ^{2}}{( x + 2 )})

3 lo g_{6} (2) + 2 lo g_{6} (x) - lo g_{6} (x + 2)

Solution steps

lo g_{6} (\frac{8 x ^{2}}{x + 2})

Apply log rule:

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

lo g_{6} (\frac{8 x ^{2}}{x + 2}) = lo g_{6} (8 x^{2}) - lo g_{6} (x + 2)

= lo g_{6} (8 x^{2}) - lo g_{6} (x + 2)

Simplify

lo g_{6} (8 x^{2}) : 3 lo g_{6} (2) + 2 lo g_{6} (x)

= 3 lo g_{6} (2) + 2 lo g_{6} (x) - lo g_{6} (x + 2)

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a^{7} + a \cdot b^{6}

What is log_{6}((8x^2)/((x+2))) ?
The solution to log_{6}((8x^2)/((x+2))) is 3log_{6}(2)+2log_{6}(x)-log_{6}(x+2)