## Enter natural log statement

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 10.8731

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
 =
 2.21888 6

x = 0.36981263747803

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.

### 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

### 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