How can I solve a equation like solve a function containint expressions like sqrt(log(x) - 1) = 2 and exp((log(x) - 1.5)**2 - 3) = 5

[Xiong Deng]

HI,

Hi, I am trying to solve an equation containing both exp, log, erfc, and
they may be embedded into each other....But sympy cannot handle this, as
shown below:

>>> from sympy import solve, exp, log, pi
>>>from sympy.mpmath import *
>>>from sympy import Symbol
>>>x=Symbol('x')
>>>sigma = 4
>>>mu = 1.5
>>>solve(x * ((1.0 / sqrt(2 * pi) * x * sigma) * exp(-0.5 * (log(x) - mu)**2
/ sigma**2)) + 0.5 * erfc((mu - log(x)) / (sigma * sqrt(2))) - 1, x)

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File
"/home/work/local/python-2.7.1/lib/python2.7/site-packages/sympy/mpmath/functions/functions.py",
line 287, in log
    return ctx.ln(x)
  File
"/home/work/local/python-2.7.1/lib/python2.7/site-packages/sympy/mpmath/ctx_mp_python.py",
line 984, in f
    x = ctx.convert(x)
  File
"/home/work/local/python-2.7.1/lib/python2.7/site-packages/sympy/mpmath/ctx_mp_python.py",
line 662, in convert
    return ctx._convert_fallback(x, strings)
  File
"/home/work/local/python-2.7.1/lib/python2.7/site-packages/sympy/mpmath/ctx_mp.py",
line 556, in _convert_fallback
    raise TypeError("cannot create mpf from " + repr(x))
TypeError: cannot create mpf from x

But sqrt, log, exp, itself is OK, as shown as below:

>>> solve((1.0 / sqrt(2 * pi) * x * sigma) - 1, x)
[0.626657068657750]

SO, How can I solve an equation containint expressions like sqrt(log(x) -
1)=0 or exp((log(x) - mu)**2 - 3) = 0??? If there are any other methods
without Sympy, it is still OK.

Thanks
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