What is log_{4}(x)-5log_{4}(y)+2log_{4}(z) ?

The solution to log_{4}(x)-5log_{4}(y)+2log_{4}(z) is log_{4}((xz^2)/(y^5))

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simplify log_{4}(x)-5log_{4}(y)+2log_{4}(z)

simplify

lo g_{4} (x) - 5 lo g_{4} (y) + 2 lo g_{4} (z)

lo g_{4} (\frac{x z ^{2}}{y ^{5}})

Solution steps

lo g_{4} (x) - 5 lo g_{4} (y) + 2 lo g_{4} (z)

- 5 lo g_{4} (y) = - lo g_{4} (y^{5})

2 lo g_{4} (z) = lo g_{4} (z^{2})

= lo g_{4} (x) - lo g_{4} (y^{5}) + lo g_{4} (z^{2})

Apply log rule:

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

lo g_{4} (x) - lo g_{4} (y^{5}) = lo g_{4} (\frac{x}{y ^{5}})

= lo g_{4} (\frac{x}{y ^{5}}) + lo g_{4} (z^{2})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{4} (\frac{x}{y ^{5}}) + lo g_{4} (z^{2}) = lo g_{4} (\frac{x}{y ^{5}} z^{2})

= lo g_{4} (\frac{x}{y ^{5}} z^{2})

Simplify

\frac{x}{y ^{5}} z^{2} : \frac{x z ^{2}}{y ^{5}}

= lo g_{4} (\frac{x z ^{2}}{y ^{5}})

ln (5) + 6 ln (x) - 5 ln (y)

ln (\frac{x}{a} \cdot e^{\frac{- x ^{2}}{( 2 a )}})

lo g_{10} (\frac{x ( x + 7 )}{( x + 3 ) ^{4}})

\frac{1}{2} lo g_{4} (16 x)

What is log_{4}(x)-5log_{4}(y)+2log_{4}(z) ?
The solution to log_{4}(x)-5log_{4}(y)+2log_{4}(z) is log_{4}((xz^2)/(y^5))