Multiple choice

What approximate value will come in place of question mark (?) in the following questions?( (5^{3})^{2.21} \times 5^{3.2} \times 25^{3.11} = 125^{13.02} \div 125^{?} )

  1. 3

  2. 8

  3. 13

  4. 19

  5. 21
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Convert all to base 5: 5^(3×2.21)×5^3.2×5^(2×3.11)=5^(6.63+3.2+6.22)=5^16.05. RHS: 125^13.02÷125^x=5^(3×13.92)÷5^(3x)=5^(41.76-3x). Equating: 16.05=41.76-3x, so 3x=25.71, x=8.57≈8.

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