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