Take the natural log of both sides, then you will have x + 2 by itself and you can easily subtract 2.
Answer
x ≈ -0.614
Example 2
Solve lnx = 50.2.
Hint
Use the inverse! Take e both sides of the equation to get x by itself.
Answer
x ≈ 6.333 × 1021
Example 3
Solve 103x = 3.
Hint
This is one of those problems where you can take the natural log of each side, even though the base is 10. It works out! Take the ln of each side, and that should leave the left side of your equation looking like ln103x which is the same as 3xln10. Keep going...you can do it.
Answer
x ≈ 0.159
Example 4
Solve elnx = 100.
Hint
Oh, you got this! The e function is an inverse already to the ln function which just leaves x on the left side.
Answer
x = 100
Example 5
Solve e-5x = 16.
Hint
Use your noggin, take the natural log'n. Take the ln of each side.
Answer
x ≈ -0.555
Example 6
Solve 5 + 2e-x = 7.
Hint
Watch out, this one's a toughy. First subtract 5 from each side, then divide by 2. Do you see it yet? Natural log it! And did you remember that the natural log of 1 is 0?
Answer
x = 0
Example 7
Solve .
Hint
First, get rid of that 3 by multiplying each side by 3. Then combine the e functions because when they are added like that, they can be combined into one product. Lastly, take the natural log of each side and get x by itself.
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