What is log_{4}((8y)/z) ?

The solution to log_{4}((8y)/z) is (log_{2}(y)+3)/2-log_{4}(z)

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simplify log_{4}((8y)/z)

simplify

lo g_{4} (\frac{8 y}{z})

\frac{lo g _{2} ( y ) + 3}{2} - lo g_{4} (z)

Solution steps

lo g_{4} (\frac{8 y}{z})

Apply log rule:

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

lo g_{4} (\frac{8 y}{z}) = lo g_{4} (8 y) - lo g_{4} (z)

= lo g_{4} (8 y) - lo g_{4} (z)

Simplify

lo g_{4} (8 y) : \frac{lo g _{2} ( y ) + 3}{2}

= \frac{lo g _{2} ( y ) + 3}{2} - lo g_{4} (z)

lo g_{10} (\frac{1}{2}) + lo g_{10} (4) - 2

ln (\frac{8}{9 x ^{9} y})

lo g_{b} (6) + lo g_{b} (4)

\frac{1}{2} ln (8) - ln (32)

ln (\frac{b}{a})

What is log_{4}((8y)/z) ?
The solution to log_{4}((8y)/z) is (log_{2}(y)+3)/2-log_{4}(z)