What is expand log_{4}((3xyz)^2) ?

The solution to expand log_{4}((3xyz)^2) is 2log_{4}(3)+2log_{4}(x)+2log_{4}(y)+2log_{4}(z)

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expand log_{4}((3xyz)^2)

expand

lo g_{4} ((3 x yz)^{2})

2 lo g_{4} (3) + 2 lo g_{4} (x) + 2 lo g_{4} (y) + 2 lo g_{4} (z)

Solution steps

lo g_{4} ((3 x yz)^{2})

Apply log rule:

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

lo g_{4} ((3 x yz)^{2}) = 2 lo g_{4} (3 x yz)

= 2 lo g_{4} (3 x yz)

Apply log rule:

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

2 lo g_{4} (3 x yz) = 2 lo g_{4} (3) + 2 lo g_{4} (x) + 2 lo g_{4} (y) + 2 lo g_{4} (z)

= 2 lo g_{4} (3) + 2 lo g_{4} (x) + 2 lo g_{4} (y) + 2 lo g_{4} (z)

6^{\frac{7 l o g _{6} ( 2 )}{2}} + 1

lo g_{10} ((\frac{7}{8})^{x})

ln (\frac{2}{sin ( θ )}) - ln (\frac{1}{sin ( θ )})

2 ln (2) - 2 ln (7)

ln (2 x^{2}) + 2 ln (x)

What is expand log_{4}((3xyz)^2) ?
The solution to expand log_{4}((3xyz)^2) is 2log_{4}(3)+2log_{4}(x)+2log_{4}(y)+2log_{4}(z)