I'd use the inverse of exponentation to do this. In other words, I'd take the log of both sides (doesn't matter if it's natural log or common log":
log 5^(2x+1) = log 25
Then (2x+1) log 5 = log 5^2
log 5^2
Then (2x+1) = ------------
log 5
Solving for 2x:
log 5^2
----------- - 1 = 2x
log 5
Now divide both sides by 2 and you'll have an expression for x.
A more elegant approach follows:
5^(2x+1) = 25 = 5^2 (now the bases are the same (5) )
Then 2x+1=2, or 2x = 1, or x = 1/2 (answer
