Question

if log x =(1/2) log y = (1/5) log z, the value of x4 y 3 z -2 is:

Answer 1

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