Question

If logX = (logy)/2 = (logZ)/5, then X^4.Y^3.Z^-3 =?

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Answer 1

Given,

log x = (log y)/2 = (log z)/5

Let,

log x = (log y)/2 = (log z)/5 = a

So,

log x = a

⇒ x = eᵃ

And,

log y = 2a

⇒ y = e^(2a)

And,

log z = 5a

⇒ z = e^(5a)

So,

x⁴ * y³ * z⁻³ = e^(4a) * e*(6a) * e^(-15a)

                  = e^(-5a)   [since, e^a * e^b = e^(a+b)]

                  = 1/e^(5a)

                  = 1/z [since e^(5a) = z]