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.
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Welcome back hkweidjatey@gmail.com — missed you this week. Here are the solutions to the problems: 5. Evaluate: _10(1,000,000) Step 1: Understand the definition of a logarithm. The expression _10(1,000,000) asks "to what power must 10 be raised to get 1,000,000?". Step 2: Express 1,000,000 as a power of 10. 1,000,000 = 10^6 Step 3: Substitute this back into the logarithm. _10(10^6) = 6 The correct option is B. B. 6 6. Simplify: 3(a) - (b) + 2(c) Step 1: Apply the power rule of logarithms, n(x) = (x^n). 3(a) = (a^3) 2(c) = (c^2) Step 2: Substitute these back into the expression. (a^3) - (b) + (c^2) Step 3: Apply the quotient rule of logarithms, (x) - (y) = ((x)/(y)). ((a^3)/(b)) + (c^2) Step 4: Apply the product rule of logarithms, (x) + (y) = (xy). ((a^3)/(b) · c^2) = ((a^3 c^2)/(b)) The correct option is A. A. ((a^3 c^2)/(b)) 9. A savings account grows by 8% each year. If the initial amount is 1000, what will it be after 2 years? Step 1: Identify the initial amount, rate, and time. Initial amount P = 1000 Annual growth rate r = 8\% = 0.08 Number of years t = 2 Step 2: Use the compound interest formula A = P(1 + r)^t. A = 1000(1 + 0.08)^2 Step 3: Calculate the value inside the parenthesis. A = 1000(1.08)^2 Step 4: Calculate (1.08)^2. A = 1000(1.1664) Step 5: Multiply to find the final amount. A = 1166.4 The correct option is B. B. 1166.4 Send me the next one 📸