# Solving a System of Equations

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Konstantinos on 11 Nov 2013
Commented: Walter Roberson on 11 Nov 2013
I am experiencing difficulties in solving the following system of equations: Υ=Χ+Α-Β*e^(-Χ/6), Υ= -10log[10^(1.76)-10^(-X/10)], where A and B are parameters defined by the user (i.e A=5, B=4). Any help could be useful. Thanks in advance!

Walter Roberson on 11 Nov 2013
You will need to solve this numerically. Subtract one from the other, numerically solve for a 0. Along the way you will need to decide if you are wanting natural logs or log10 .
Caution: this is pretty sensitive numerically, especially near X = -17.6
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Walter Roberson on 11 Nov 2013
eqn1 = sym('OBO=IBO+A-B*exp(IBO/6)');
eqn2 = sym('10^(-IBO/10)+10^(-OBO/10)=10^1.76');
sA = sym('A');
sB = sym('B');
seqn1 = subs(eqn1, {sA, sB}, {A, B});
seqn2 = subs(eqn2, {sA, sB}, {A, B});
solve(seqn1, seqn2)

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