Solving Exponencial fuction is not returning the right answer

How do i solve this exponencial:

12734.40 == 12000 * 1.02^x

i am doing:

solve(12734.4 == 12000*1.02^x,x

and getting log(2653/2500) / log(51/50)

the answer shoud be a 3.

Answer 1

[John D'Errico]

Yes, you THINK the true answer is 3. But it is not.

format long g
log(2653/2500) / log(51/50)

ans = 
          2.99961931278214

And that is effectively the exact answer (to 16 significant digits) to the problem you posed. You could have made MATLAB convert that number to a floating point number, using either vpa or double.

What would the true left hand side have been, if 3 had been the correct result?

12000*sym('1.02')^3

ans = 

12734.496

So you had 12734.40 in the equation you tried to solve. Should MATLAB have solved a different problem than the one you posed? Surely not! MATLAB cannot know that you only had approximate coefficients, and that you expected an integer result. At least not unless you tell it to look for an approximate solution using some more appropriate solution method.

For example, if I use a solver that can constrain the unknown to be an integer, minimizing the absolute error, I get this:

fun = @(x) 12734.40 - 12000*1.02.^x;
lb = 0;
[xval,fval,exitflag] = ga(@(x) abs(fun(x)),1,[],[],[],[],lb,[],[],1)

Optimization terminated: average change in the penalty fitness value less than options.FunctionTolerance
and constraint violation is less than options.ConstraintTolerance.

xval = 
     3

fval = 
        0.0960000000013679

exitflag = 
     1

Here MATLAB was able to find an integer solution.

[Rodrigo Toledo]

@William Rose @John D'Errico Thanks for the answers and to explain to me that what i was assuming is wrong. Thanks guys. Its much clear to me now. xD

[William Rose]

You're elcome Rodrigo.

Answer 2

[William Rose]

Algebra:

x=log(12734/12000)/log(1.02)

>> x=log(12734/12000)/log(1.02)
x =
    2.9980
>>

[Rodrigo Toledo]

I know the algebra. I just want matlab to solve it, using solve or other function without the need to put in the log form.

[William Rose]

@Rodrigo Toledo,

Sorry about that. I think Matlab thinks it did solve it. Maybe you and I would disagree.

Matlab "simplified" 1.02 to 51/50 and it simplified the other side similarly. The answer does not exactlyy equal three. I bet that is why Matlab does not simplify any farther.

[Rodrigo Toledo]

another issue i am facing with matlab: trying to get x=2 and y=3 for this equation:

@syms x y
eq = x^2 + y^3 = 31
solve(eq)

any tips?

thx

[William Rose]

@Rodrigo Toledo, I am not familiar with Matlab's symbolic math routines. I don't know if you can instruct Matlab to restrict the solution space to ℤ (or restrict it to ℝ).