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# Symbolic calculation and to solve out a variable

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Pouyan Msgn on 11 Mar 2020
Closed: MATLAB Answer Bot on 20 Aug 2021
I have the equation :
I_1=2.15 ; I_2=8.625;
n2=0.039; n1=0.1;
L_1=16.76*10^-10
L_2=15.56*10^-10;
I tried with this code but it is wrong:
clc
clear all
syms I1 I2 n1 n2 L1 L2 d
I_1=2.15 ; I_2=8.625;
n2=0.039; n1=0.1;
L_1=16.76*10^-10
L_2=15.56*10^-10;
I1/I2=((n1*L1)/(n2*L2))*(1-exp(-d/L1))/(exp(-d/L2));
I want to solve d

Steven Lord on 11 Mar 2020
Write your last line as an equation and use solve.
Walter Roberson on 11 Mar 2020
vpasolve(I_1/I_2==((n1*L_1)/(n2*L_2))*(1-exp(-d/L_1))/(exp(-d/L_2)), d)

Ameer Hamza on 11 Mar 2020
Edited: Ameer Hamza on 11 Mar 2020
First, your syntax is incorrect, as pointed out in Steven's answer. However, if you correct the syntax, the solve will still not be able to provide the solution because an analytical solution does not exist for such equations.
Your other choice is to use a numerical solver, such as fsolve. However, because of the scale of L_1 and L_2, and their presence in the exponent, directly using fsolve will get you nowhere. Therefore, you first need to scale the exponent and then apply fsolve. See the code
I_1=2.15 ; I_2=8.625;
n2=0.039; n1=0.1;
L_1=16.76*10^-10;
L_2=15.56*10^-10;
f = @(d) I_2/I_1*((n1*L_1)/(n2*L_2))*(1-exp(-d/L_1*10^-10))/(exp(-d/L_2*10^-10)) - 1;
d = fsolve(f, 1)*10^-10;
Here, I first scaled the exponents by a factor of 10^-10 and corrected the final solution by scaling again.