e) Solve for given

To solve for in the equation , we can rewrite 8 as a power of 2. Since , we can set the exponents equal to each other:

Solving for , we add 2 to both sides:

Thus, the solution is .

Now, a handy tip for working with equations involving exponents is to always look for a way to express both sides using the same base. This approach can simplify the problem immensely! Also, a common mistake is to overlook the base conversion, which can lead to incorrect assumptions about the relationship between the terms. Always double-check your transformations!