Question

if a^2=b^3=c^5=d^6 then show that log (abc) base d =31/5​

Answer 1

let a² = b³ = c⁵ = d⁶ = f

a² = f

a = f^(1/2)

b³ = f

b = f^(1/3)

c⁵ = f

c = f^(1/5)

d⁶ = f

d = f^(1/6)

log (base d) abc

= log (base f^(1/6) (f^(1/2) * f^(1/3) * f^(1/5))

= log (base f^(1/6) (f^(1/2 + 1/3 + 1/5))

= log (base f^(1/6) (f^(31/30)

= 31/30 log (base f^(1/6) f

= (31/30 ÷ 1/6) log (base f) f

= (31/5) log (base f) f

= (31/5) (1)

= 31/5

Answer 2

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