Pls solve the question given in the image with explanation.
Answers
Answer:
Step-by-step explanation:
60ᵃ = 3
//Take log to base 60 on both sides
Log₆₀60ᵃ = Log₆₀3
=> a = Log₆₀3
60ᵇ = 5
//Take log to base 60 on both sides
Log₆₀60ᵇ = Log₆₀5
=> b = Log₆₀5
Now we need to find value of 12 ¹⁻ᵃ⁻ᵇ/2(1-b)
First simplify the value in the power:
1 - a - b/2(1-b) 1 -(a+b)/2(1-b) = 1 - (Log₆₀3 + Log₆₀5) / 2 ( 1 - Log₆₀5)
= 1 - Log₆₀15 / 2 ( 1 - Log₆₀5)
= Log₆₀60 - Log₆₀15 / 2 (Log₆₀60 - Log₆₀5)
= Log₆₀(60/15) / 2 * Log₆₀(60/5)
= Log₆₀4 / 2Log₆₀12
= 2Log₆₀2/2Log₆₀12
= Log₆₀2 / Log₆₀12
= Log₁₂2.
So 12 ¹⁻ᵃ⁻ᵇ/2(1-b) = (12)∧ Log₁₂2 = 2.