# Solve an exponencial equation

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Emanuel Thiago on 15 Apr 2021
Answered: Alan Stevens on 16 Apr 2021 at 8:28
There is my code:
syms k
Mp = exp((-3.8./sqrt(6.784-1221.21*k))./(1-14.44./6.784-1221.21*k)) == 0.07;
s = solve(Mp)
the result:
s =
(1099511627776*root(359552000*z1^3*log(7)*log(10) - 359552000*z1^3*log(10)^2 - 89888000*z1^3*log(7)^2 - 1627664768*z1^2*log(7)*log(10) + 1627664768*z1^2*log(10)^2 + 406916192*z1^2*log(7)^2 - 5047535724*z1*log(7)*log(10) + 1261883931*z1*log(7)^2 + 5047535724*z1*log(10)^2 - 3106559808*log(7)*log(10) + 3106559808*log(10)^2 + 776639952*log(7)^2 - 1297982720, z1, 1))/1342734594956329
(1099511627776*root(359552000*z1^3*log(7)*log(10) - 359552000*z1^3*log(10)^2 - 89888000*z1^3*log(7)^2 - 1627664768*z1^2*log(7)*log(10) + 1627664768*z1^2*log(10)^2 + 406916192*z1^2*log(7)^2 - 5047535724*z1*log(7)*log(10) + 1261883931*z1*log(7)^2 + 5047535724*z1*log(10)^2 - 3106559808*log(7)*log(10) + 3106559808*log(10)^2 + 776639952*log(7)^2 - 1297982720, z1, 2))/1342734594956329
(1099511627776*root(359552000*z1^3*log(7)*log(10) - 359552000*z1^3*log(10)^2 - 89888000*z1^3*log(7)^2 - 1627664768*z1^2*log(7)*log(10) + 1627664768*z1^2*log(10)^2 + 406916192*z1^2*log(7)^2 - 5047535724*z1*log(7)*log(10) + 1261883931*z1*log(7)^2 + 5047535724*z1*log(10)^2 - 3106559808*log(7)*log(10) + 3106559808*log(10)^2 + 776639952*log(7)^2 - 1297982720, z1, 3))/1342734594956329
So, i want to matlab solve a that exponencial equation "exp((-3.8./sqrt(6.784-1221.21*k))./(1-14.44./6.784-1221.21*k)) == 0.07", in k terms, witch i already solve on paper, but the answear is not expected i guess, at least i dont know what to do with that, my answear on paper was -1.653*10^-2, i read on forums that i should use solve function in the way i used in the code, i dont know if im doing something wrong, i would be very gratefull if someone help me.

Alan Stevens on 16 Apr 2021 at 8:28
Plot a graph of your function first, to see roughly where the root is, then use fzero:
f = @(k) exp((-3.8./sqrt(6.784-1221.21*k))./(1-14.44./6.784-1221.21*k)) - 0.07;
k0 = -2*10^-3;
k = fzero(f,k0);
format long
disp(k)
-0.001327715853814
x = -2*10^-3:10^-5:-10^-3;
plot(x,f(x), k,f(k),'o'),grid