If 2 ^π‘Ž β‹… 2^ 𝑏 = 3^ 𝑐 , what is the value of π‘Ž + 𝑏/ 𝑐 ?

If 2 ^π‘Ž β‹… 2^ 𝑏 = 3^ 𝑐 , what is the value of π‘Ž + 𝑏/ 𝑐 ?

Explanation
  • 2aβ‹…2b=2a+b2^a cdot 2^b = 2^{a + b}, so the equation becomes 2a+b=3

  • This is only possible when both sides equal 1 β‡’a + b = 0,.

  • So, a+bc=00frac{a + b}{c} = frac{0}{0}Β which is undefined.