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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?
1. 18
2. 15
3. 12
4. 5

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Correct Answer - Option 4 : 5

 \(x^{(y^{z} )}=1 \) …… (i)

∴ x = 1, because for any value of yz

If x = 1, then, \(x^{y^{z} }\) remain 1.

∴ x = 1

  \(y^{z^{x }}=125\)…… (ii)

We can verify value from this equation by putting x = 1, y = 5 and z = 3

\(5^{3^{1}}=125\)

Again,

 \(z^{y^{x}}=243 \) …… (iii)

\(z^{y^{x}}=3^{5^{1}}=243\)

∴ It is clear that –

⇒ x = 1, y = 5 and z = 3

The value of 9x + 10y – 18z

⇒ 9 + 50 – 54

⇒ 5

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