Math, asked by khuranaprisha2008, 5 months ago

Pls solve the question given in the image with explanation.

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Answers

Answered by spiderman2019
1

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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