Question 21

If $$X^{y^z} = 1, Y^{z^x} = 125$$ and $$Z^{y^x} = 243$$ ($$X, Y$$ and $$Z$$ are natural numbers), then what is the value of $$9X + 10Y - 18Z$$?

Solution

$$X^{y^z} = 1$$ this equation derives that 1 to the power of any thing is always 1.

So, X=1.

Now,

$$Y^{z^x}=125\ \ implies\ that\ Y^Z=5^3$$

And,

$$Z^Y=243\ implies\ that\ Z^Y=3^5.$$

So, Y=5 and Z=3.

So, $$9X+10Y-18Z=9\times1+10\times5-18\times3=59-54=5.$$

D is correct choice.

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