The lowest value of $x$ that satisfies the equation is $3 \times 3^{4/7}$, which simplifies to approximately 5.43.

Would you like a more detailed breakdown of the steps? Here are some related questions to explore further:

1. What are the steps to convert logarithms to a different base?
2. How do we simplify expressions involving logarithmic equations?
3. How does the change of base formula work?
4. How can logarithmic identities help solve equations like this?
5. What are some applications of solving logarithmic equations?

Tip: When solving logarithmic equations, always check if the domain of the solution matches the constraints of the logarithm, ensuring the argument stays positive.