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 — Here's how to simplify the expression: f) Simplify _10 3sqrt(3) Step 1: Rewrite the argument of the logarithm, 3sqrt(3), as a single power of 3. Recall that sqrt(3) = 3^1/2. 3sqrt(3) = 3^1 × 3^1/2 Using the exponent rule a^m × a^n = a^m+n: 3^1 × 3^1/2 = 3^1 + (1)/(2) = 3^(2)/(2) + (1)/(2) = 3^(3)/(2) Step 2: Substitute this back into the logarithm. _10 (3^(3)/(2)) Step 3: Apply the logarithm power rule, _b (x^p) = p _b x. _10 (3^(3)/(2)) = (3)/(2) _10 3 The simplified expression is (3)/(2) _10 3. Send me the next one 📸