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# x,y , and z are positive real numbers

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If x,y , and z are positive real numbers satisfying:

log(x/y) = a

log(y/z)  = 15

log(z/x) = -1

Find a.

Oct 19, 2020

#1
+11086
+1

If x,y , and z are positive real numbers satisfying:

log(x/y) = a

log(y/z)  = 15

log(z/x) = -1

Hello Guest!

$$log(\frac{x}{y})=a\\ log(\frac{y}{z})=15\\ log(\frac{z}{x})=-1$$

$$log(x)-log(y)=a\\ log(y)-log(z)=15\\ log(z)-log(x)=-1$$

$$X-Y=a\\ Y-Z=15\\ Z-X=-1$$

$$Z=X-1$$

$$Y=X-a=15-Z\\ a=X+Z-15\\ a=X+X-1-15\\a=2X-16$$

$$a=log(x^2)-16$$

!

Oct 19, 2020