I understand the issue from the problem statement. Based on my knowledge of SymPy's printing system and the detailed issue description, I can create the necessary patch. The issue is about two main inconsistencies:

1. `exp(-x)*log(x)` - LaTeX prints `\frac{1}{e^{x}} \log{...}` instead of `e^{-x} \cdot \log(x)`
2. `1/(x + y)/2` - LaTeX prints `\frac{1}{2x + 2y}` instead of `\frac{1}{2(x + y)}`

The problem is in the `_print_Mul` method of the `LatexPrinter` class. The LaTeX printer is:
1. Converting negative exponents to fractions when it shouldn't always do so
2. Distributing denominators across terms when it shouldn't

Let me provide the patch based on the SymPy codebase structure and the typical implementation patterns:

--- a/sympy/printing/latex.py
+++ b/sympy/printing/latex.py
@@ -381,7 +381,8 @@ def _print_Mul(self, expr):
 
         # Check for unevaluated Mul. In this case we need to make sure the
         # temporary variables are distinct from the rest of the expression
-        args = [str(arg) for arg in expr.args]
+        from sympy.core.mul import _keep_coeff
+        from sympy.core.power import Pow
 
         include_parens = False
         if _coeff_isneg(expr):
@@ -398,12 +399,25 @@ def _print_Mul(self, expr):
 
         a = []  # items in the numerator
         b = []  # items in the denominator (if any)
+        for item in args:
+            if item.is_commutative and item.is_Pow and item.exp.is_Rational and item.exp.is_negative:
+                if item.exp != -1:
+                    b.append(Pow(item.base, -item.exp, evaluate=False))
+                else:
+                    b.append(Pow(item.base, -item.exp))
+            elif item.is_Rational and item is not S.Infinity:
+                if item.p != 1:
+                    a.append(Rational(item.p))
+                if item.q != 1:
+                    b.append(Rational(item.q))
+            else:
+                a.append(item)
 
-        if self.order not in ('old', 'none'):
-            args = expr.as_ordered_factors()
-        else:
-            args = list(expr.args)
-
+        # if there are no factors in the numerator, add a 1
+        if not a:
+            a.append(S.One)
+        
         # If quantities are present append them at the back of the product
         args = sorted(args, key=lambda x: isinstance(x, Quantity) or
                       (isinstance(x, Pow) and isinstance(x.base, Quantity)))

This is getting complex. Let me analyze the actual reported issue more carefully and provide a targeted fix. The key issues are:

1. For `exp(-x)*log(x)`: The LaTeX printer converts `e^(-x)` to `1/e^x` form
2. For `1/(x+y)/2`: The LaTeX printer combines `1/2` and `1/(x+y)` into `1/(2x+2y)` by distributing

Based on the SymPy source code structure and the typical fix for this kind of issue:

--- a/sympy/printing/latex.py
+++ b/sympy/printing/latex.py
@@ -381,8 +381,7 @@ class LatexPrinter(Printer):
         from sympy.core.power import Pow
         from sympy.core.mul import Mul
 
-        include_parens = False
-        if _coeff_isneg(expr):
+        if _coeff_isneg(expr):
             expr = -expr
             tex = "- "
             if expr.is_Add:
@@ -394,59 +393,71 @@ class LatexPrinter(Printer):
         # Build up a list of elements in the numerator and denominator
         # and identify if we need to use a fraction or not.
 
-        a = []  # items in the numerator
-        b = []  # items in the denominator (if any)
+        numer, denom = [], []
 
         if self.order not in ('old', 'none'):
             args = expr.as_ordered_factors()
         else:
             args = list(expr.args)
 
-        # If quantities are present append them at the back of the product
-        args = sorted(args, key=lambda x: isinstance(x, Quantity) or
-                      (isinstance(x, Pow) and isinstance(x.base, Quantity)))
-
+        # Separate into numerator and denominator
         for item in args:
-            if _coeff_isneg(item):
-                if item == -1:
-                    continue
-                a.append(-item)
-            elif item.is_commutative and item.is_Pow and item.exp.is_Rational and item.exp.is_negative:
-                if item.exp != -1:
-                    b.append(Pow(item.base, -item.exp, evaluate=False))
+            if item.is_commutative and item.is_Pow:
+                if item.exp.is_Rational and item.exp.is_negative:
+                    if item.exp != -1:
+                        denom.append(Pow(item.base, -item.exp, evaluate=False))
+                    else:
+                        denom.append(item.base)
                 else:
-                    b.append(Pow(item.base, -item.exp))
-            elif item.is_Rational and item is not S.Infinity:
+                    numer.append(item)
+            elif item.is_Rational and item is not S.Infinity and item.p != S.NegativeOne:
                 if item.p != 1:
-                    a.append(Rational(item.p))
+                    numer.append(Rational(item.p))
                 if item.q != 1:
-                    b.append(Rational(item.q))
+                    denom.append(Rational(item.q))
             else:
-                a.append(item)
+                numer.append(item)
 
-        # From here it suffices to print both a and b as a Mul
-        a_str = [self._print(x) for x in a]
-        b_str = [self._print(x) for x in b]
+        if not numer:
+            numer.append(S.One)
 
-        # Check if we can separate out signs
-        if a_str[0] == r"\left(-1\right)" or a_str[0] == "-1":
-            a_str[0] = "-"
-            if len(a_str) == 1:
-                a_str[0] = "-1"
+        # Convert to strings
+        numer_str = [self._print(x) for x in numer]
+        denom_str = [self._print(x) for x in denom]