Question

Find the value of y if \(3y^{log_{3}2}+2^{log_{3}y}=log_381\)
1. 1
2. 30
3. 2
4. 3

Answer 1

Correct Answer - Option 1 : 1

Concept:

• \(a^{log_{b}x}=x^{log_{b}a}\) where b ≠ 1, a and x are positive integers.
• \({log_{a}x}= b\Rightarrow x=a^b\)

Calculation:

Given: \(3y^{log_{3}2}+2^{log_{3}y}=log_381\)

As we know that, \(a^{log_{b}x}=x^{log_{b}a}\) where b ≠ 1, a and x are positive integers.

⇒ \(3 \times 2^{log_{3}y}+2^{log_{3}y}=log_33^4\)

⇒ \(4 \times 2^{log_{3}y}=4log_33\)

⇒ \(4 \times 2^{log_{3}y}=4\)

⇒ \(2^{log_{3}y}=1 = 2^0\)

⇒ \({log_{3}y} = 0\)

⇒ y = 3⁰ = 1

Hence, option A is correct.