This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — let's solve this logarithmic equation. Given the equation: _x 10^3 = 3 Step 1: Simplify the term 10^3. _x 1000 = 3 Step 2: Convert the logarithmic equation into its equivalent exponential form. The definition of a logarithm states that _b a = c is equivalent to b^c = a. Applying this to our equation, where b=x, a=1000, and c=3: x^3 = 1000 Step 3: Solve for x by taking the cube root of both sides. x = [3]1000 x = 10 Step 4: Check the validity of the solution. For a logarithm _b a, the base b must be positive and b ≠ 1. Our solution x=10 satisfies these conditions (10 > 0 and 10 ≠ 1). The value of x is 10. What's next? 📸