Q61 / 180 · COMEDK 2022 · Mathematics
The value of $3^{\log _4 5}-5^{\log _4 3}$ is
- Correct answerA0
- B1
- C2
- D4
Solution
Let $x = 3^{\log_{4} 5} - 5^{\log_{4} 3}$.
Using the property of logarithms $a^{\log_{b} c} = c^{\log_{b} a}$, we compare the two terms.
The first term is $3^{\log_{4} 5}$.
The second term is $5^{\log_{4} 3}$.
Applying the property $a^{\log_{b} c} = c^{\log_{b} a}$ to the second term, we get $5^{\log_{4} 3} = 3^{\log_{4} 5}$.
Therefore, $x = 3^{\log_{4} 5} - 3^{\log_{4} 5} = 0$.
Answer: 0
Using the property of logarithms $a^{\log_{b} c} = c^{\log_{b} a}$, we compare the two terms.
The first term is $3^{\log_{4} 5}$.
The second term is $5^{\log_{4} 3}$.
Applying the property $a^{\log_{b} c} = c^{\log_{b} a}$ to the second term, we get $5^{\log_{4} 3} = 3^{\log_{4} 5}$.
Therefore, $x = 3^{\log_{4} 5} - 3^{\log_{4} 5} = 0$.
Answer: 0
Hence, the correct answer is option: 'A'.