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
To evaluate the expression, we will use the properties of logarithms. We assume the base of the logarithm is 10, as is common when no base is specified and '1' appears in the expression. Step 1: Simplify the numerator 4 - 25. Using the logarithm property a - b = (a)/(b): 4 - 25 = (4)/(25) We can also write (4)/(25) as ((2)/(5))^2. So, the numerator is ((2)/(5))^2. Step 2: Simplify the denominator 1 + 2 (1)/(5). First, use the property (1)/(x) = - x: (1)/(5) = - 5 Substitute this into the denominator: 1 + 2(- 5) = 1 - 2 5 Now, express '1' as a logarithm with base 10: 1 = 10. 10 - 2 5 Using the property b a = a^b: 10 - (5^2) = 10 - 25 Using the property a - b = (a)/(b): 10 - 25 = (10)/(25) Simplify the fraction: (10)/(25) = (2)/(5) So, the denominator simplifies to (2)/(5). Step 3: Substitute the simplified numerator and denominator back into the original expression. The expression becomes: ( (2)/(5))^2 (2)/(5) Using the property a^b = b a for the numerator: (2 2)/(5) (2)/(5) Step 4: Cancel out the common term. Since (2)/(5) is a common term in both the numerator and the denominator, and (2)/(5) ≠ 1, (2)/(5) ≠ 0. We can cancel it out. (2 2)/(5) (2)/(5) = 2 The final answer is 2. Send me the next one 📸