1. **State the problem:** Solve for $x$ in the equation $\log_{10}(x) = 0.508754358631946$. 2. **Recall the definition of logarithm:** $\log_a(b) = c$ means $a^c = b$. Here, $a=10$, $c=0.508754358631946$, and $b=x$. 3. **Rewrite the equation using the definition:** $$x = 10^{0.508754358631946}$$ 4. **Calculate the value:** Using a calculator or approximation, $$x \approx 10^{0.508754358631946} \approx 3.23$$ 5. **Conclusion:** The solution to the equation is approximately $$\boxed{3.23}$$