Solve for X: ln(x) + ln(x+1) = 1

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In summary, the conversation discusses solving the equation ln(x) + ln(x+1) = 1 by converting it to e^1 = x^2 + x and then using the quadratic formula to solve for x.
  • #1
r_swayze
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Im having trouble finding the solution to this problem, can anyone walk me through this?

So far I have:

ln(x) + ln(x+1) = 1

ln(x)(x+1) = 1

e^1 = x(x+1)

e^1 = x^2 + x

This is where I get stuck.
Am I on the right track?
 
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  • #2
r_swayze said:
e^1 = x^2 + x

Yes this is correct. Write e^1 as just e, which is constant.
If you move it to the other side you'll get:
x2+x-e =0

Now how do you solve the equation ax2+bx+c=0?
 
  • #3
rock.freak667 said:
Yes this is correct. Write e^1 as just e, which is constant.
If you move it to the other side you'll get:
x2+x-e =0

Now how do you solve the equation ax2+bx+c=0?

I don't think x^2 + x - e = 0 can factor out, at least not without using the quadratic formula
 
  • #4
r_swayze said:
I don't think x^2 + x - e = 0 can factor out, at least not without using the quadratic formula

Then use the wquadratic equation formula and you'd solve for x.
 

1. What is the meaning of "ln" in the equation?

ln stands for natural logarithm, which is the inverse function of the exponential function. It is used to calculate the power to which the base (e) must be raised to obtain a given number. In this equation, ln(x) represents the natural logarithm of x.

2. How do I solve for x in this equation?

To solve for x, you can use the properties of logarithms to rewrite the equation as a single logarithm. In this case, you can combine the two logarithms using the product rule, which states that ln(a) + ln(b) = ln(ab). Therefore, the equation can be rewritten as ln(x(x+1)) = 1. Then, you can take the inverse of the natural logarithm, which is the exponential function, to both sides to get x(x+1) = e. This can be solved using algebraic methods to obtain the value of x.

3. Can this equation be solved for x using a calculator?

Yes, this equation can be solved using a calculator by using the inverse function of the natural logarithm, which is the exponential function. Most scientific calculators have a button for the natural logarithm (ln) and the exponential function (e^x) to make this process easier.

4. Are there any restrictions on the values of x in this equation?

Yes, since the natural logarithm is only defined for positive numbers, x and (x+1) must both be greater than 0. This means that the possible solutions for x are between 0 and infinity.

5. How can this equation be applied in real life situations?

This equation can be applied in situations involving exponential growth or decay, such as population growth, interest rates, or radioactive decay. It can also be used to solve for the time or rate of change in these scenarios.

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