Solving an equation with log

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Rafi B
Rafi B 2021-3-20
评论： Walter Roberson 2021-3-20
Hi i'm fairly new to MATLAB and encounter a problem regarding this equation y=c(x)^m
where m is the gradient of points:
(x,1y1)=(100,50)
(x2,y2)=(1000,10)
This is the eq i put on MATLAB:
Eq = log10(Y2) == log10(C1*X2^(m)); %Equation
C1 = vpasolve (Eq, C1)
It seems that i get C far from my hand-drawn answer
How to solve C?

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Walter Roberson
Walter Roberson 2021-3-20
Ran in:
Looks okay to me.
format long g
X1 = 100; Y1 = 50;
X2 = 1000; Y2 = 10;
m = (Y2-Y1)./(X2-X1);
syms C1
Eq = log10(Y2) == log10(C1*X2^(m)); %Equation
C1sol = solve(Eq,C1)
C1sol = 
vpa(C1sol)
ans = 
13.593563908785257310765717430783
%log10(Y2) == log10(C1*X2^m) implies
%Y2 == C1*X2^m implies
C1_numeric = Y2/(X2^m)
C1_numeric =
13.5935639087853
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Rafi B
Rafi B 2021-3-20
quick question, on eqn3 wouldn't it just cross the c value off?
Walter Roberson
Walter Roberson 2021-3-20
Yes, giving you an equation of the form A=B^m with known A and B, which you can use to find m easily.

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