The value of 3^ ₄ 5 -5^ ₄ 3 is

Step-by-step solution

Let x = 3^ ₄ 5 - 5^ ₄ 3 . Using the property of logarithms a^ _ b c = c^ _ b a , we compare the two terms. The first term is 3^ ₄ 5 . The second term is 5^ ₄ 3 . Applying the property a^ _ b c = c^ _ b a to the second term, we get 5^ ₄ 3 = 3^ ₄ 5 . Therefore, x = 3^ ₄ 5 - 3^ ₄ 5 = 0 . Answer: 0