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To solve the equation , we can start by isolating . Rearranging gives us . As approaches negative infinity, the right side approaches 0, but since is strictly positive for all real , we need to look only at for potential solutions and analyze it graphically for quicker insights.

Now, for the expression , we can simplify this by expressing each base in terms of powers of 3 and 2. Notice that , , and . By plugging in these expressions and simplifying, we can combine similar terms to have a cleaner result that highlights how exponents add when bases are the same. This will lead you to a final simplified expression that you can interpret easily.

For the equation , take note that and , which will help you express everything in terms of a uniform base for easier handling. The numerator can be combined effectively once you rewrite as and consolidate the whole expression under a common theme—this often opens up cancellation opportunities.

Lastly, for , factor out from the numerator to harness the power of simplification. This lets you express everything in a more digestible way—much to the relief of your mathematical endeavors! Remember, simplifying before diving into calculations can save time and help avoid common pitfalls.