How do I solve this equation: 2^a+3^a=32.?

Question

I wanted the algebric resolution

Answer 1

I don't immediately see how to solve this one algebraically.

I graphed the function 2^x+3^x-32 on a graphing calculator, and looked for the root: it turns out to be around 2.9108011.

Answer 2

You need to find what the variable (a) equals.  Because the variables are both a's they need to be the same number so you need to find a number you can replace both variables with.

example.  

2^a+3^a=32

2^3+3^3=32 (this this not the correct answer, it equals 35)