What is expand log_{12}(sqrt((y^4)/(zm^4))) ?

The solution to expand log_{12}(sqrt((y^4)/(zm^4))) is 2log_{12}(y)-2log_{12}(m)-1/2 log_{12}(z)

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expand log_{12}(sqrt((y^4)/(zm^4)))

expand

lo g_{12} (\frac{y ^{4}}{z m ^{4}})

2 lo g_{12} (y) - 2 lo g_{12} (m) - \frac{1}{2} lo g_{12} (z)

Solution steps

lo g_{12} (\frac{y ^{4}}{z m ^{4}})

\frac{y ^{4}}{z m ^{4}} = \frac{y ^{2}}{m ^{2} z}

= lo g_{12} (\frac{y ^{2}}{m ^{2} z})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{12} (\frac{y ^{2}}{m ^{2} z}) = lo g_{12} (y^{2}) - lo g_{12} (m^{2} z)

= lo g_{12} (y^{2}) - lo g_{12} (m^{2} z)

Simplify

lo g_{12} (y^{2}) : 2 lo g_{12} (y)

lo g_{12} (m^{2} z) = 2 lo g_{12} (m) + \frac{1}{2} lo g_{12} (z)

= 2 lo g_{12} (y) - (\frac{1}{2} lo g_{12} (z) + 2 lo g_{12} (m))

- (2 lo g_{12} (m) + \frac{1}{2} lo g_{12} (z)) : - 2 lo g_{12} (m) - \frac{1}{2} lo g_{12} (z)

= 2 lo g_{12} (y) - 2 lo g_{12} (m) - \frac{1}{2} lo g_{12} (z)

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(2 x - 2 y) d x + (y - 1) d y

\frac{2}{( s - 3 ) ( s ^{2} + 4 )}

What is expand log_{12}(sqrt((y^4)/(zm^4))) ?
The solution to expand log_{12}(sqrt((y^4)/(zm^4))) is 2log_{12}(y)-2log_{12}(m)-1/2 log_{12}(z)