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
Here's the solution for the logarithmic expression: The expression is Log_e e^2 + Log_3 243 - Log_625 25. Step 1: Evaluate the first term, Log_e e^2. The natural logarithm Log_e is denoted as . Using the property (e^x) = x: Log_e e^2 = e^2 = 2 Step 2: Evaluate the second term, Log_3 243. We need to express 243 as a power of 3. 3^5 = 243 So, using the property Log_b b^x = x: Log_3 243 = Log_3 3^5 = 5 Step 3: Evaluate the third term, Log_625 25. We need to express both 625 and 25 as powers of the same base. 25 = 5^2 625 = 25^2 = (5^2)^2 = 5^4 So the term becomes Log_5^4 5^2. Using the property Log_b^k A^m = (m)/(k) Log_b A: Log_5^4 5^2 = (2)/(4) Log_5 5 Since Log_5 5 = 1: (2)/(4) · 1 = (1)/(2) Step 4: Combine the evaluated terms. 2 + 5 - (1)/(2) 7 - (1)/(2) To subtract, find a common denominator: (14)/(2) - (1)/(2) = (13)/(2) The simplified value of the expression is: (13)/(2) 3 done, 2 left today. You're making progress.