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.