如何在 Excel Solver 上求解这个指数方程？

Question

100e^0.25*y = 97.5

Solving for y

Using Excel Solver

I tried using empty column entry for y in 'By changing cells' and Set objective function as LHS of above equation (empty column entry in equation included) equal to value of 97.5 in solver.

It gives no solution

How do I do this?

Answer 1

You don't really need the solver. Just re-arrange your formula to solve for Y. Since y = b^x is the same as log(b)Y = x (log of Y , with base b )

Your formula above is the same as:

Y = (log(100e)97.5))/.25

(Read aloud, that's log of 97.5, with base 100e, divided by .25

So, Y = 3.268305672

(Bonus points for someone who can tell me how to format this so the Log looks correct)

Answer 2

It's a bit ambiguous what you're asking...

• Literal math interpretation: 100*(e^0.25)*y = 97.5

  Then y = 97.5 / ( 100 * exp(.25)) = .759

• My guess of what you want: 100*e^(0.25*y) = 97.5

  Then y = ln(97.5/100) / .25 = -.101

• Another possibility: (100 * e)^(0.25 * y) = 97.5

  Then y = (ln(97.5) / ln(100*e)) / .25 = 3.268

Whatever it is, this doesn't need solver!

Answer 3

The question is "How do I solve this exponential equation on Excel Solver?" which is a fair enough question, as it points to trying to understand how to set up solver.

My interpretation of the equation provided is given in this screenshot ...

The solver dialog box is then setup as follows ...

Of note:

• This is a non-linear equation and needs GRG Nonlinear. If you choose LP Simplex, it will not pass the linearity test.
• Ensure "Make Unconstrained Variables Non-Negative" is not checked.

It provided this result for me ...

A more precise answer can be obtained by decreasing the "Convergence" value on the GRG Non-Linear Options dialog.

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A problem this simple can also be solved using Goal Seek.