ln(2x+1)=10?

Question

the answer they give is x= (e^10 - 1)/(2), but i do not know how they came to this.

Answer 1

The log of a number to a given base is the power to which the base must be raised to give the number.
In this example:-
base is e
number is 2x + 1
Thus
e^10 = 2x + 1
2x = e^10 - 1
x = (1/2) (e^10 - 1)

Answer 2

Recall two things:
- The base of ln is e
- ln a = b ---> e^b = a

ln(2x + 1) = 10
Definition of ln:
e^10 = 2x + 1
Subtract 1 from both sides:
e^10 - 1 = 2x
Divide both sides by 2:
(e^10 - 1) / 2 = x

Answer 3

first you must know that ln (number) = power then (number )= e^power as the base is e
then2x+1= e^10=22026.46576 then 2x= e^10 - 1 divide by 2 then x= (e^10 - 1)/(2)
or numerically
then 2x = 22026.46576 - 1 = 22025.46576
then x =11012.73288

Answer 4

Hey there!

Here's the answer.

ln(2x+1)=10 --> Write the problem.
2x+1=e^10 --> Change the base on each equation to e or take the "anti-log" on both sides of the equation. Then use the formula e^ln(x)=x, on the left side of the equation.
2x=e^10-1 --> Subtract 1 on both sides of the equation.
x=(e^10-1)/2 Divide 2 on both sides of the equation.

So the answer is x=(e^10-1)/2.

Hope it helps!

Answer 5

there is a matematic rule

ln a = b is the same e^(ln a) = e^b

and e^(ln a) = a

in this example:

ln (2x+1) = 10
e^(ln (2x+1) = e^10
2x+1 = e^10
x = (e^10-1)/2

Greetings

Answer 6

ln(2x+1) = 10 = lne^10
2x+1 = e^10
x = (e^10 - 1)/(2)

Answer 7

change to exponential form

e^10 = 2x+1

or 2x + 1 = e^10

2x = e^10 - 1

x = (e^10 - 1)/2

Answer 8

Logarithm is a transformation used to solve mathematical equations involving exponents. In convention ln(x) refers to the logarithm of 'x' with base 'e' (natural number).
The above equation comes from that relationship only.