Correct Answer - Option 1 : 27
Concept:
-
\(a^{log_{b}x}=x^{log_{b}a}\) where b \(\neq\)1, a, x are positive integers.
- \({log_{a}x}= b\Rightarrow x=a^b\)
Calculation:
Given: \(7y^{log_{3}2}+2^{log_{3}y}=64\)
As we know that, \(a^{log_{b}x}=x^{log_{b}a}\) where b \(\neq\)1, a, x are positive integers.
⇒ \(7 \times 2^{log_{3}y}+2^{log_{3}y}=64\)
⇒ \(8 \times 2^{log_{3}y}=64\)
⇒ \(2^{log_{3}y}=8=2^3\)
⇒ \({log_{3}y}=3\)
⇒ y = 33
⇒ y = 27
Hence, option A is correct.