show me step bt step on how to solve this problem. don't use [and { in the steps.

Question

(3094/r)=5927(((1+r)^27)/r)

Answer 1

To solve the equation (3094/r) = 5927(((1+r)^27)/r), we will follow these steps:

1. Eliminate the fraction: Multiply both sides by r to get rid of the denominator: 3094 = 5927 * (1 + r)^27

2. Isolate the term with the variable: Divide both sides by 5927: (3094/5927) = (1 + r)^27

3. Simplify the left side: Calculate the fraction and express it in decimal form: x = 3094/5927 x ≈ 0.522

   Now the equation looks like: 0.522 = (1 + r)^27

4. Take the 27th root: To isolate (1 + r), take the 27th root of both sides: 1 + r = (0.522)^(1/27)

5. Calculate the right side: Using a calculator to find the 27th root: 1 + r ≈ 0.998

6. Isolate r: Subtract 1 from both sides: r ≈ 0.998 - 1 r ≈ -0.002

7. Result: Therefore, the solution is: r ≈ -0.002, or in percentage terms, r ≈ -0.2%.

Remember to check the initial equation using this value of r to ensure that the solution is valid.