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What value should come in place of the question mark (??) in the following equation? (13.311.21)3.5÷(1.1)4.5×(1.331)2=(1.1)?3(\frac{13.31}{1.21})^{3.5} \div (1.1)^{-4.5} \times (1.331)^{2} = (1.1)^{? - 3}

What value should come in place of the question mark (??) in the following equation? (13.311.21)3.5÷(1.1)4.5×(1.331)2=(1.1)?3(\frac{13.31}{1.21})^{3.5} \div (1.1)^{-4.5} \times (1.331)^{2} = (1.1)^{? - 3}

  1. 1414

  2. 1717

  3. 1111

  4. 1515

  5. 1919

Show answer & explanation

Correct answer

1717

Explanation

Convert all bases to 1.11.1: 13.311.21=(1.1)3(1.1)2=(1.1)1\frac{13.31}{1.21} = \frac{(1.1)^3}{(1.1)^2} = (1.1)^1 So, [(1.1)1]3.5=(1.1)3.5[(1.1)^1]^{3.5} = (1.1)^{3.5}. Next, ÷(1.1)4.5=×(1.1)4.5\div (1.1)^{-4.5} = \times (1.1)^{4.5}. (1.331)2=[(1.1)3]2=(1.1)6(1.331)^2 = [(1.1)^3]^2 = (1.1)^6. Left side: (1.1)3.5+4.5+6=(1.1)14(1.1)^{3.5 + 4.5 + 6} = (1.1)^{14}. Right side: (1.1)?3(1.1)^{? - 3}. Equating exponents: 14=?3    ?=1714 = ? - 3 \implies ? = 17.

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