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Mathematics

The value of (log 8 - log 2) ÷ log 32 is :

  1. 25\dfrac{2}{5}

  2. 52\dfrac{5}{2}

  3. 2

  4. 4

Logarithms

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Answer

Simplifying the expression :

(log 8 - log 2) ÷ log 32log 8 - log 2log 32log 23log 2log 253 log 2 - log 25 log 22 log 25 log 225.\Rightarrow \text{(log 8 - log 2) ÷ log 32} \\[1em] \Rightarrow \dfrac{\text{log 8 - log 2}}{\text{log 32}} \\[1em] \Rightarrow \dfrac{\text{log 2}^3 - \text{log 2}}{\text{log 2}^5} \\[1em] \Rightarrow \dfrac{\text{3 log 2 - log 2}}{\text{5 log 2}} \\[1em] \Rightarrow \dfrac{\text{2 log 2}}{\text{5 log 2}} \\[1em] \Rightarrow \dfrac{2}{5}.

Hence, Option 1 is the correct option.

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