how to solve this equation

Question

If 6^a *2^b=3^x what is 2^a+b?

Answer 1

6^a2^b = 3^x But, 6^a = (2•3)^a = 2^a3^a

So, we have 2^a3^a2^b = 2^a+b3^a = 3^x

So, 2^a+b = 3^x-a

The only power of 3 that is also a power of 2 is 3⁰ = 1.

Therefore, 2^a+b = 1