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
You have 2 free calculationss remaining
What is the Answer?
x = 0.36981263747803
How does the Logarithms and Natural Logarithms and Eulers Constant (e) Calculator work?
Free Logarithms and Natural Logarithms and Eulers Constant (e) Calculator - This calculator does the following:
* Takes the Natural Log base e of a number x Ln(x) → logex
* Raises e to a power of y, ey
* Performs the change of base rule on logb(x)
* Solves equations in the form bcx = d where b, c, and d are constants and x is any variable a-z
* Solves equations in the form cedx=b where b, c, and d are constants, e is Eulers Constant = 2.71828182846, and x is any variable a-z
* Exponential form to logarithmic form for expressions such as 53 = 125 to logarithmic form
* Logarithmic form to exponential form for expressions such as Log5125 = 3
This calculator has 1 input.
* Takes the Natural Log base e of a number x Ln(x) → logex
* Raises e to a power of y, ey
* Performs the change of base rule on logb(x)
* Solves equations in the form bcx = d where b, c, and d are constants and x is any variable a-z
* Solves equations in the form cedx=b where b, c, and d are constants, e is Eulers Constant = 2.71828182846, and x is any variable a-z
* Exponential form to logarithmic form for expressions such as 53 = 125 to logarithmic form
* Logarithmic form to exponential form for expressions such as Log5125 = 3
This calculator has 1 input.
What 8 formulas are used for the Logarithms and Natural Logarithms and Eulers Constant (e) Calculator?
Ln(a/b) = Ln(a) - Ln(b)
Ln(ab)= Ln(a) + Ln(b)
Ln(e) = 1
Ln(1) = 0
Ln(xy) = y * ln(x)
For more math formulas, check out our Formula Dossier
Ln(ab)= Ln(a) + Ln(b)
Ln(e) = 1
Ln(1) = 0
Ln(xy) = y * ln(x)
For more math formulas, check out our Formula Dossier
What 4 concepts are covered in the Logarithms and Natural Logarithms and Eulers Constant (e) Calculator?
- euler
- Famous mathematician who developed Euler's constant
- logarithm
- the exponent or power to which a base must be raised to yield a given number
- natural logarithm
- its logarithm to the base of the mathematical constant e
eLn(x) = x - power
- how many times to use the number in a multiplication
Example calculations for the Logarithms and Natural Logarithms and Eulers Constant (e) Calculator
Logarithms and Natural Logarithms and Eulers Constant (e) Calculator Video
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