Why does $2^(x+1) + 2^(x+1) = 2^(x+2)$ but $3^(x+1) + 3^(x+1) != 3^(x+2)$ ?

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Answer 1 · 2016-04-23T00:20:44

See explanation...

For any $a > 0$ we find:

$a^(x+1) + a^(x+1) = 2*a^(x+1)$

Also:

$a*a^(x+1) = a^1*a^(x+1) = a^(1+x+1) = a^(x+2)$

So when $a = 2$ we have:

$2^(x+1)+2^(x+1) = 2 * 2^(x+1) = 2^(x+2)$

When $a=3$ we have:

$3^(x+1)+3^(x+1) = 2 * 3^(x+1)$

Why does 2^(x+1) + 2^(x+1) = 2^(x+2)2^(x+1) + 2^(x+1) = 2^(x+2) but 3^(x+1) + 3^(x+1) != 3^(x+2)3^(x+1) + 3^(x+1) != 3^(x+2) ?