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Mathematics

The value of log 8−log 2log 32\dfrac{\text{log} \space 8 - \text{log} \space 2}{\text{log} \space 32} is

  1. 25\dfrac{2}{5}

  2. 14\dfrac{1}{4}

  3. −25-\dfrac{2}{5}

  4. 13\dfrac{1}{3}

Logarithms

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Answer

Given,

⇒log 8−log 2log 32⇒log 23−log 2log 25⇒3log 2−log 25log 2⇒2log 25log 2⇒25.\Rightarrow \dfrac{\text{log} \space 8 - \text{log} \space 2}{\text{log} \space 32} \\[1em] \Rightarrow \dfrac{\text{log} \space 2^3 - \text{log} \space 2}{\text{log} \space 2^5} \\[1em] \Rightarrow \dfrac{3\text{log} \space 2 - \text{log} \space 2}{5\text{log} \space 2} \\[1em] \Rightarrow \dfrac{2 \text{log} \space 2}{5\text{log} \space 2} \\[1em] \Rightarrow \dfrac{2}{5}.

Hence, Option 1 is the correct option.

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