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
1a) Simplify e^ x^2. Step 1: Use the property e^ a = a. e^ x^2 = x^2 The expression is defined for x ≠ 0. The simplified expression is x^2. 1b) Simplify 4 + 25. Step 1: Use the logarithm property a + b = (ab). 4 + 25 = (4 × 25) Step 2: Perform the multiplication. = 100 Step 3: Evaluate the logarithm. Assuming base 10 for . = 2 The simplified expression is 2. 2a) Solve for x in the equation 3 x + (x)/(2) = 4. Step 1: Apply the logarithm property a b = b^a. x^3 + (x)/(2) = 4 Step 2: Apply the logarithm property a + b = (ab). ( x^3 · (x)/(2) ) = 4 ( (x^4)/(2) ) = 4 Step 3: Convert the logarithmic equation to an exponential equation. Assuming base 10 for . (x^4)/(2) = 10^4 Step 4: Solve for x^4. (x^4)/(2) = 10000 x^4 = 2 × 10000 x^4 = 20000 Step 5: Solve for x. x = [4]20000 x = [4]2 × 10^4 x = 10 [4]2 For the logarithms to be defined, x > 0. The solution $10 [4]2