program MetodNuytona;
const eps = 1e-6;
var x,x0: real;
Function f(x: real): real;
begin
f:=ln(exp(ln(2)*x)-5)/ln(3)+ln(exp(ln(2)*x)-7)/ln(3)-1;
end;
Function f1(x: real): real;
begin
f1:=exp(ln(2)*x)*ln(2)/((exp(ln(2)*x)-5)*ln(3)+exp(ln(2)*x)*ln(2))/((exp(ln(2)*x)-5)*ln(3));
end;
Begin
writeln;
writeln('Решение нелинейного уравнения f(x)=0');
writeln;
write('x0 = ');
read(x0);
writeln;
x:=x0;
repeat
x:=x-f(x)/f1(x);
until abs(f(x)/f1(x))<eps;
writeln('Метод Ньютона**:');
writeln;
writeln('x=',x:8:5);
End.

program MetodNuytona;
uses math;
const
   eps = 1e-6;


function f(x: real): real;
begin
   writeln('x = ', x:10:5,
           '| 2^x - 5 = ', (power(2, x) - 5):10 :5,
           '| 2^x - 7 = ', (power(2, x) - 7):10 :5);
   f := logn(3, power(2, x) - 5) +
        logn(3, power(2, x) - 7) - 1;
end;
function f1(x: real): real;
begin
   f1 := ( power(2, x + 1) * (power(2, x) - 6) * ln(2) ) /
         ( (power(2, x) - 7) * (power(2, x) - 5) * ln(3) );
end;

var
   x, x0 : real;
begin
   writeln;
   writeln('Решение нелинейного уравнения f(x)=0');
   writeln;
   write('x0 = '); readln(x0);
   writeln;
   x:=x0;
   repeat
      x:=x-f(x)/f1(x);
   until abs(f(x)/f1(x))<eps;
   writeln('Метод Ньютона**:');
   writeln;
   writeln('x=',x:8:5);
end.

Решение нелинейного уравнения f(x)=0

x0 = 5

x =    5.00000| 2^x - 5 =   27.00000| 2^x - 7 =   25.00000
x =    1.83035| 2^x - 5 =   -1.44377| 2^x - 7 =   -3.44377
An unhandled exception occurred at $0040FD20 :
EInvalidOp : Invalid floating point operation