Logarithmic Equation D51Be2

1. **State the problem:** Solve the logarithmic equation $$\log_{10}(2x) = 3$$. 2. **Recall the definition of logarithm:** $$\log_{10}(y) = z$$ means $$10^z = y$$. 3. **Apply the definition:** From $$\log_{10}(2x) = 3$$, we get $$10^3 = 2x$$. 4. **Calculate:** $$10^3 = 1000$$, so $$1000 = 2x$$. 5. **Solve for $$x$$:** $$x = \frac{1000}{2}$$ 6. **Simplify:** $$x = \cancel{\frac{1000}{\cancel{2}}} = 500$$. 7. **Check the solution:** Substitute $$x=500$$ back into the original equation: $$\log_{10}(2 \times 500) = \log_{10}(1000) = 3$$, which is true. **Final answer:** $$x = 500$$.