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Evaluate \(x\) for  \(\frac{{\log 256}}{{\log 16}} = \log x\) 
1. 1000
2. 100
3. 200
4. 500
5. 300

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Correct Answer - Option 2 : 100

Concept:

  • \({\log _a}b = \frac{{\log b}}{{\log a}}\)

Calculation:

 Given: \(\frac{{\log 256}}{{\log 16}} = \log x\)

\(⇒ \frac{{\log {{\left( {16} \right)}^2}}}{{\log \left( {16} \right)}} = \log x\)

As we know that, \({\log _a}b = \frac{{\log b}}{{\log a}}\) and \({\log _a}{a^n} = n\) where a ≠ 1

⇒ 2 = log x

Raising both sides to the power 10, we get

⇒ x = 102

⇒ x = 100

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