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Mathematics

If log x - log (2x - 1) = 1, the value of x is :

  1. 1910\dfrac{19}{10}

  2. 19 × 10

  3. 1019\dfrac{10}{19}

  4. 119×10\dfrac{1}{19 \times 10}

Logarithms

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Answer

Given,

⇒log x−log (2x−1)=1⇒log x2x−1=log 10⇒x2x−1=10⇒x=10(2x−1)⇒x=20x−10⇒20x−x=10⇒19x=10⇒x=1019.\Rightarrow \text{log } x - \text{log } (2x - 1) = 1 \\[1em] \Rightarrow \text{log } \dfrac{x}{2x - 1} = \text{log } 10 \\[1em] \Rightarrow \dfrac{x}{2x - 1} = 10 \\[1em] \Rightarrow x = 10(2x - 1) \\[1em] \Rightarrow x = 20x - 10 \\[1em] \Rightarrow 20x - x = 10 \\[1em] \Rightarrow 19x = 10 \\[1em] \Rightarrow x = \dfrac{10}{19}.

Hence, Option 3 is the correct option.

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