Question

If a² = b⁴ = c⁶ = d¹⁰ then find value of log_d (abc)

1. 53/1
2. 59/7
3. 0
4. 55/6

Answer 1

Correct Answer - Option 4 : 55/6

Calculation:

a² = b⁴ = c⁶ = d¹⁰

⇒ a² = d¹⁰

⇒ a = d^{(10/ 2)}

⇒ a = d⁵

Similarly, b = d^5/2 and c = d^5/3

⇒ log_d (d⁵ × d^5/2 × d^5/3)

⇒ d⁵ × d^5/2 × d^5/3

⇒ d^{5 + (5/2) + (5/3)}

⇒ 55/6

∴ required answer is 55/6

log_d (d) = 1