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Given that
log x =(1/2) log y = (1/5) log z
Taking first and second term, we get
log x =(1/2) log y
⇒ logy = 2logx
⇒ logy = logx²
⇒ y = x² ...(1)
Taking first and third term, we get
log x = (1/5) log z
⇒ logz = 5logx
⇒ logz = logx⁵
⇒ z = x⁵ ...(2)
Now evaluate x⁴y³z⁻²
x⁴y³z⁻² = x⁴(x²)³(x⁵)⁻² [ using (1) and (2) ]
= x⁴x⁶x⁻¹⁰
= x¹⁰⁻¹⁰ = x⁰
x⁴y³z⁻² = 1
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