*insert joke about walking to the dungeon uphill in the snow both ways*
Okay, now we've got that out of the way...
I recommend simply adjusting your XP awards. If you want PCs to level up after 50 encounters instead of 10, cut your XP awards to 1/5 normal. Simple as that. (Or do what a lot of us have taken to doing and just tell your players they level up when you damn well feel like it.)
Second, I think you're misremembering: In 2e and 3e it took precisely 13 encounters of an equal level to get from level 1 to level 2. Note, that 2e uses approximately a quadratic xp progression, while 3e and 4e use a linear progression. This means it took progressively longer to advance further, while it takes about the same time, now.
You're both misremembering and getting the math wrong, dude. First of all, in 2E, it did not take "precisely 13 encounters" to level up--it didn't take precisely
anything to level up, because different classes leveled at different rates. At 2,000 XP, the fighter was level 2, the cleric was level 2 plus a bit, the thief was more than halfway to level 3, and the poor wizard was still poking along at level 1.
Second, 2E and 4E both have roughly exponential (geometric) XP tables; the amount of XP required to reach level N+1 is approximately K times the amount of XP required to reach level N. In 2E, K is 2, although you see a lot of variation from the baseline at levels in the high single digits, and sometime around level 9-12 (depending on class) it levels off and becomes a linear (arithmetic) progression, with fixed XP per level*. In 4E, K is the fourth root of 2. There's some rounding to make the numbers look pretty, but otherwise it's a smooth exponential curve all the way up.
3E has a quadratic XP table. The amount of XP required to reach level N is equal to (N^2 - N) * 500.
[size=-2]*Side note: This leveling-off would in theory cause a 2E PC's advancement to start
accelerating once you hit name level; you continue to fight tougher foes and get bigger treasures as you level up, with correspondingly larger XP awards, but you only need the same amount of XP to advance. In practice, the difference wasn't noticeable, at least to me. But then, I never got past level 14 or so. The folks with characters in the 50+ range might disagree.[/size]