Natural Logarithms Quiz Part 1

1. Solve the equation ln(x) = 2 for x.

To solve for x, we need to exponentiate both sides of the equation using the natural exponential function (e):

e^(ln(x)) = e^2

x = e^2

So, x is approximately equal to 7.389.

2. Evaluate ln(1).

The natural logarithm of 1 is 0. Therefore, ln(1) = 0.

3. Simplify ln(e^3).

The natural logarithm of e raised to any power is simply that power. Therefore, ln(e^3) = 3.

4. Solve the equation ln(x) = 0.5 for x.

Using the same method as in question 1:

e^(ln(x)) = e^0.5

x = e^0.5

So, x is approximately equal to 1.649.

5. Evaluate ln(10).

The natural logarithm of 10 is approximately 2.303. Therefore, ln(10) ≈ 2.303.