# Solve 0=0.002*e^-(0.005/2R) to Find R

• Josh123
In summary, the conversation is discussing how to find the value of "R" in the equation 0=0.002*e^-(0.005/2R). The person is struggling to find a solution and asks for tips. It is clarified that there is no solution as e^(x) is always greater than 0. However, if the number is small but not zero, the solution is to divide both sides by 0.0005, take the natural logarithm, and solve for R.
Josh123
Hello. I am working on this problem

0=0.002*e^-(0.005/2R)

I am supposed to find to find "R". The only way I know how to do this gives me 0... but I know that it's not the answer. Got any tips?

There is no solution.

e^(x) > 0 for every x. This should clarify the point made by James R

What if the number is small (but not zero)... ie 0.000001 = 0005e^(0.004/2R)

Josh123 said:
What if the number is small (but not zero)... ie 0.000001 = 0005e^(0.004/2R)

Then it's easy (and NOT "Calculus and Analysis"!). Divide both sides by 0.0005 to get $$e^{\frac{0.004}{2R}}= \frac{0.000001}{0.0005}$$.

Take the natural logarithm of both sides to get rid of the exponential:
$$\frac{0.004}{2R}= ln(\frac{0.000001}{0.0005})$$

Multiply both sides by R:
$$0.002= R ln(\frac{0.000001}{0.0005})$$
and, finally, divide both sides by the logarithm:

$R= \frac{0.002}{ln(\frac{0.000001}{0.0005}}$

Last edited by a moderator:

## What is the equation being solved?

The equation being solved is 0=0.002*e^-(0.005/2R).

## What is the purpose of solving this equation?

The purpose of solving this equation is to find the value of R, which is a constant in the equation.

## What does 0=0.002*e^-(0.005/2R) represent?

This equation represents the relationship between two variables, 0 and R, where R is a constant.

## What is the significance of the constant e in the equation?

The constant e, also known as Euler's number, is a mathematical constant that is used to represent growth or decay in a variety of scientific and mathematical equations.

## How can this equation be solved to find the value of R?

This equation can be solved by isolating the variable R on one side of the equation and using algebraic techniques to solve for its value.

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