How do you condense this expression into a single logarithm? $\frac{{log}_{5} x}{2} + \frac{{log}_{5} y}{2} + \frac{{log}_{5} z}{2}$ $log_(5)x/2+log_(5)y/2+log_(5)z/2$

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Answer 1 · 2016-12-03T19:08:52

The Answer is ${log}_{5} \sqrt{x y z}$ $log_5sqrt(xyz)$ .

$\frac{{log}_{5} x}{2} + \frac{{log}_{5} y}{2} + \frac{{log}_{5} z}{2}$ $(log_5x)/2+(log_5y)/2+(log_5z)/2$ .

$= \frac{1}{2} [{log}_{5} x + {log}_{5} y + {log}_{5} z]$ $=1/2[log_5x+log_5y+log_5z]$ .

$= \frac{1}{2} [{log}_{5} (x) \times (y) \times (z)]$ $=1/2[log_5(x)xx(y)xx(z)]$ .

$= \frac{1}{2} {log}_{5} x y z$ $=1/2log_5xyz$ .

$= {log}_{5} {(x y z)}^{\frac{1}{2}}$ $=log_5(xyz)^(1/2)$ .

$= {log}_{5} \sqrt{x y z}$ $=log_5sqrt(xyz)$ . (Answer).

How do you condense this expression into a single logarithm? log_(5)x/2+log_(5)y/2+log_(5)z/2log5x2+log5y2+log5z2log_(5)x/2+log_(5)y/2+log_(5)z/2