Solving Equation for Lambda in Terms of A

  • Thread starter ACLerok
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In summary, the conversation is about solving for the variable lambda in terms of A. The person is unsure how to proceed after multiplying the denominator term to the other side and is seeking advice on how to get rid of the exponential terms. Suggestions are given to take the log of both sides or use logical reasoning to conclude that the bases on each side are equal. It is also mentioned that exponential is a one-to-one function. After cancelling the ln's, the person ends up with an equation where it seems that the lambdas cancel each other out, but it is clarified that this is not the case according to the solutions. A hint is given to expand the binomial on the RHS to simplify and solve for lambda in terms of A.
  • #1
ACLerok
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I am trying to solve for the variable lambda in terms of A. After multiplying the denominator term over to the other side, how do I go on from there? I don't know how to get rid of the exponential terms.

Thanks on advance.

http://img521.imageshack.us/img521/4006/picture1ug1.th.png [Broken]
 
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  • #2
You can take the log of both sides
 
  • #3
Or, you can use logical reasoning to conclude that if the bases on each side are equal, then...?
 
  • #4
"the bases on each side are equal" and exponential is a one-to-one function!
 
  • #6
ACLerok said:
After cancelling the ln's I end up with the equation below, but then it seems the lambdas cancel each other out. Is that correct? apparently from the solutions, lambda does not cancel.
http://img516.imageshack.us/img516/5822/picture1nd7.th.png [Broken]

You're equation looks correct so far, but you can reduce it to lamba in terms of A.

Hint: Expand the binomial on the RHS.
 
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What is the formula for solving an equation for lambda in terms of A?

The formula for solving an equation for lambda in terms of A is λ = A.

Can any equation be solved for lambda in terms of A?

No, not all equations can be solved for lambda in terms of A. Only equations that have a lambda variable and an A variable can be solved in this way.

What is the purpose of solving an equation for lambda in terms of A?

The purpose of solving an equation for lambda in terms of A is to find the value of lambda in relation to A. This can help with further calculations or understanding the relationship between the two variables.

What are the steps for solving an equation for lambda in terms of A?

The steps for solving an equation for lambda in terms of A are:

  1. Isolate the lambda variable on one side of the equation.
  2. Divide both sides by the coefficient of lambda, if necessary.
  3. Simplify the equation, if possible.
  4. Replace any remaining A variables with the given value.
  5. Solve for lambda.

Can solving an equation for lambda in terms of A be used in real-world applications?

Yes, solving an equation for lambda in terms of A can be used in various real-world applications such as physics, chemistry, and engineering. It can help in understanding the relationship between two variables and making predictions or calculations based on the given values.

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