Pls solve the question given in the image with explanation.

1.	Pls solve the question given in the image with explanation.
Answer» 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.

Answer»

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.

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