# how to find value of variable in natural logarithmic

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ibrahim alzoubi on 30 Apr 2021
Commented: ibrahim alzoubi on 30 Apr 2021
How to find value of X:
ln(X/0.466)*66.66+X*4.4805*10^(-4)+X=5.66
Scott MacKenzie on 30 Apr 2021
hint #1: e^(ln(x)) = x
hint #2: e^(ln(y) + ln(z)) = y * z

DGM on 30 Apr 2021
Edited: DGM on 30 Apr 2021
This can be done a number of ways. It's a log plus a positive linear function of x. There will be only one solution. That makes everything easier.
% solving symbolically
syms X
eqn = log(X/0.466)*66.66+X*4.4805*10^(-4)+X==5.66;
aaa = double(solve(eqn,X))
% or using fsolve
f = @(x) log(x/0.466)*66.66 + x*4.4805*10^(-4) + x - 5.66;
bbb = fsolve(f,1)
% or using fzero
ccc = fzero(f,1)
% do the answers make sense? check it graphically
x = linspace(0.2,1,100);
y = log(x/0.466)*66.66 + x*4.4805*10^(-4) + x;
plot(x,y); hold on
plot([0.2 1],[1 1]*5.66)
plot(aaa,5.66,'bo')
plot(bbb,5.66,'ko','markersize',10) ibrahim alzoubi on 30 Apr 2021
does the value of X is 0.5035?