Solving a System of Equations

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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!

Accepted Answer

Walter Roberson
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
Walter Roberson
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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