Evaluate the following logarithmic expression
4e^6x=100
Evaluate e
Since we have e = 2.718281828459, a becomes 10.873127313836
We need to divide each side of the equation by 10.873127313836
| 4e6x | |
| 10.873127313836 |
| = |
| 100 |
| 10.873127313836 |
e6x = 9.1969860292861
Take the natural log of both sides
Ln(e6x) = Ln(9.1969860292861)
Use a logarithmic identity
Ln(an) = n * Ln(a)
Using that identity, we have
n = 6x and a = e, so our equation becomes:
6xLn(e) = 2.2188758248682
Given that e = 2.718281828459, we have:
6x * Ln(2.718281828459)
Evaluate outside constant
(6 * 1)x = 2.2188758248682
6x = 2.2188758248682
Divide each side of the equation by 6
| 6x | |
| 6 |
| = |
| 2.2188758248682 |
| 6 |
Final Answer
x = 0.36981263747803
