To solve the problem, we need to identify the base used in a common logarithm.
1. Understanding Common Logarithms:
A common logarithm is a logarithm with base 10. It is usually written as $ \log x $ without explicitly showing the base.
2. Definition:
The expression $ \log x $ refers to $ \log_{10} x $, which means "the power to which 10 must be raised to get $x$."
3. Conclusion:
Since the base of the common logarithm is 10, the correct answer is 10.
Final Answer:
The base of the common logarithm is $ \mathbf{10} $.
The product of all solutions of the equation \(e^{5(\log_e x)^2 + 3 = x^8, x > 0}\) , is :