enigmatic puzzle - Treasure hunt 'round the world! (clue 2)

If you're interested in starting the treasure hunt from the very beginning, check out the prologue!

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Upon arrival at the Pamplona Airport, you head towards baggage claim. Standing at baggage claim, you see a man in a suit and sunglasses. One hand is behind his back; in the other, he holds a sign that reads "[insert username here]". Walking up to him, you say:

"Hi. My name is [insert username here]. Do you have something for me?"

Without hesitation, he stretches the arm from behind his back out towards you. In it he holds a small envelope. You take the envelope and eagerly tear it open, pulling another small card out from inside. The card reads:

Dear [insert username here],

Congratulations on your arrival in Pamplona! I'd suggest you stay and enjoy the city (it is a beautiful city), but there's no time for that - you're running a race! Grab your bag, rent a car, and hit the road! This time, you're driving to your next location, which is (more or less) detailed on the back of this letter.

Yours truly,

Bailey M
Puzzlemaster for the Treasure Hunt 'Round the World

You flip over the letter and read:

Lisbon, Portugal: 7.3498737047383369

Knockainey, Ireland: 7.2723983925700463
Boudekak, Algeria: 6.8394764382288426

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As you circle in on the answer, make careful note of your location. At some point down the line, you'll be left with two. Don't look too closely here, as your first instinct will most likely be correct. Once you've centered in on the solution, the final destination (much like the above numbers) should feel natural.

As you finish reading, you notice your suitcase drop onto the conveyor belt. Time to grab that bag and hit the road!

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Where is your next destination?

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The story continues in the next part, Treasure hunt 'round the world! (Interlude 1)

Answer

The final destination is:

Definitely throw PrincessTrevor a +1 for posting the logarithm portion first.

The portion of the letter that says:

the final destination (much like the above numbers) should feel natural.

implies that the numbers listed above are natural logarithms. These numbers correspond to:

Lisbon, Portugal 1556
Knockainey, Ireland 1440
Boudekak, Algeria 934

Some other portions of the letter:

As you circle in on the answer

implies that we should be looking for circles.

Drawing circles on the map with the radius listed above and at the locations in Google maps gives this image:

At some point down the line, you'll be left with two

is referring to, Toledo, Spain and Turin, Italy because they lie at the intersection of two of the circles and is inside the third.

At some point down the line, you'll be left with two. Don't look too closely here, as your first instinct will most likely be correct. Once you've centered in on the solution, the final destination

The final destination lies halfway on a line between Toledo and Turin.

Once you've centered in on the solution, the final destination (much like the above numbers) should feel natural.

The final destination:

Parc Natural de la Vall de Sorteny is pretty "natural"