To solve for $x$ in the equation:

$\log x = -4$

we assume the logarithm is base 10 unless another base is specified. This can be rewritten in exponential form:

$x = 10^{-4}$

Calculating $10^{-4}$:

$x = \frac{1}{10^4} = 0.0001$

So, the solution is:

$x = 0.0001$

Would you like further explanation on logarithmic properties or steps?

Here are some related questions you might explore:

1. What is the process for solving logarithmic equations with different bases?
2. How do we handle logarithmic equations with additional terms, such as $\log(x+2) = -4$?
3. Can you explain the relationship between exponential and logarithmic functions?
4. How would the solution change if the equation were $\ln x = -4$ (natural logarithm)?
5. What are some real-life applications of solving logarithmic equations?

Tip: When converting from logarithmic to exponential form, remember that $\log_b a = c$ implies $a = b^c$.