I need help proving a math question ! (logarithms)

[annaaxo]

If a^x + a^y = a^w + a^z,
does x + y = w + z ?
If so, show proof.

I'm not sure if this can be proven correctly or not, but it was brought up by my math teacher because I used it on a test and got the right answer, even though it wasn't a general property.

(Test question that I solved using this) :
3^2x + 3^x - 12 = 0
3^2x + 3^x = 12
3^2x + 3^x = 3^2 + 3^1
2x + x = 2 + 1
3x = 3
x = 1

 

[Romsek]

No. What you did was just lucky.

 

[Harry_the_cat]

Here's a counter-example to disprove the statement.

\(\displaystyle 1^3+1^2=1^4+1^5\) BUT \(\displaystyle 3+2\neq4+5\)