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
Step 1: Simplify the terms on the left-hand side (LHS) using the logarithm power rule, n a = a^n. The LHS is 2 4 + (1)/(2) 25 - 20. 2 4 = 4^2 = 16 (1)/(2) 25 = 25^1/2 = sqrt(25) = 5 Substitute these back into the LHS: LHS = 16 + 5 - 20 Step 2: Combine the terms using the logarithm product rule, a + b = (ab). 16 + 5 = (16 × 5) = 80 Now the LHS is: LHS = 80 - 20 Step 3: Combine the remaining terms using the logarithm quotient rule, a - b = ((a)/(b)). LHS = ((80)/(20)) = 4 Step 4: Simplify the right-hand side (RHS) using the logarithm power rule. The RHS is 2 2. RHS = 2^2 = 4 Step 5: Compare the simplified LHS and RHS. We found LHS = 4 and RHS = 4. Since LHS = RHS, the statement is shown to be true. LHS = 4 = RHS 3 done, 2 left today. You're making progress.