What is expand log_{6}(6x^3y^4) ?

The solution to expand log_{6}(6x^3y^4) is 1+3log_{6}(x)+4log_{6}(y)

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expand log_{6}(6x^3y^4)

expand

lo g_{6} (6 x^{3} y^{4})

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

Solution steps

lo g_{6} (6 x^{3} y^{4})

Apply log rule:

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

lo g_{6} (6 x^{3} y^{4}) = lo g_{6} (6) + lo g_{6} (x^{3}) + lo g_{6} (y^{4})

= lo g_{6} (6) + lo g_{6} (x^{3}) + lo g_{6} (y^{4})

Apply log rule:

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

lo g_{6} (x^{3}) = 3 lo g_{6} (x)

= lo g_{6} (6) + 3 lo g_{6} (x) + lo g_{6} (y^{4})

Apply log rule:

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

lo g_{6} (y^{4}) = 4 lo g_{6} (y)

= lo g_{6} (6) + 3 lo g_{6} (x) + 4 lo g_{6} (y)

Apply log rule:

lo g_{a} (a) = 1

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

ln (\frac{sin ( x )}{x ^{2}})

ln (sin (9) x^{3})

ln (m^{2} e^{m x})

lo g_{10} (18.4 \cdot 1 0^{12}) - 6

ln (\frac{2 t}{t ^{4} + 2 t + 1})

What is expand log_{6}(6x^3y^4) ?
The solution to expand log_{6}(6x^3y^4) is 1+3log_{6}(x)+4log_{6}(y)