What is log_{6}((64x^3(4x+1))/(2x-1)) ?

The solution to log_{6}((64x^3(4x+1))/(2x-1)) is 6log_{6}(2)+3log_{6}(x)+log_{6}(4x+1)-log_{6}(2x-1)

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simplify log_{6}((64x^3(4x+1))/(2x-1))

simplify

lo g_{6} (\frac{64 x ^{3} ( 4 x + 1 )}{2 x - 1})

6 lo g_{6} (2) + 3 lo g_{6} (x) + lo g_{6} (4 x + 1) - lo g_{6} (2 x - 1)

Solution steps

lo g_{6} (\frac{64 x ^{3} ( 4 x + 1 )}{2 x - 1})

Apply log rule:

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

lo g_{6} (\frac{64 x ^{3} ( 4 x + 1 )}{2 x - 1}) = lo g_{6} (64 x^{3} (4 x + 1)) - lo g_{6} (2 x - 1)

= lo g_{6} (64 x^{3} (4 x + 1)) - lo g_{6} (2 x - 1)

Simplify

lo g_{6} (64 x^{3} (4 x + 1)) : 6 lo g_{6} (2) + 3 lo g_{6} (x) + lo g_{6} (4 x + 1)

= 6 lo g_{6} (2) + 3 lo g_{6} (x) + lo g_{6} (4 x + 1) - lo g_{6} (2 x - 1)

lo g_{10} (b) + 2 lo g_{10} (c)

lo g_{2} (\frac{2}{y})

lo g_{10} (\frac{x}{100000})

ln (b) - ln (a)

lo g_{6} (x) - lo g_{6} (x^{5})

What is log_{6}((64x^3(4x+1))/(2x-1)) ?
The solution to log_{6}((64x^3(4x+1))/(2x-1)) is 6log_{6}(2)+3log_{6}(x)+log_{6}(4x+1)-log_{6}(2x-1)