Solve for x; 11. Use logarithms table to evaluate rac86.4 imes 0.410.013

Here are the solutions to the problems: 10. Solve for x a) 3^x-5 = 9 Step 1: Express both sides with the same base. 3^x-5 = 3^2 Step 2: Equate the exponents. x-5 = 2 Step 3: Solve for x. x = 2+5 x = 7 The value of x is 7. b) 2^x-1 = 8^2x+3 Step 1: Express both sides with the same base. 2^x-1 = (2^3)^2x+3 Step 2: Apply the power rule (a^m)^n = a^mn. 2^x-1 = 2^3(2x+3) 2^x-1 = 2^6x+9 Step 3: Equate the exponents. x-1 = 6x+9 Step 4: Solve for x. x - 6x = 9 + 1 -5x = 10 x = (10)/(-5) x = -2 The value of x is -2. 11. Use logarithms table to evaluate (86.4 × 0.41)/(0.013) Let N = (86.4 × 0.41)/(0.013). Step 1: Take the logarithm of both sides. N = ((86.4 × 0.41)/(0.013)) Step 2: Apply logarithm properties (ab) = a + b and ((a)/(b)) = a - b. N = 86.4 + 0.41 - 0.013 Step 3: Find the logarithms of each number (using a calculator as a proxy for a log table). 86.4 = 1.9365 0.41 = 1.6128 (which is -1 + 0.6128) 0.013 = 2.1139 (which is -2 + 0.1139) Step 4: Perform the addition and subtraction. N = 1.9365 + (1.6128) - (2.1139) N = 1.9365 - 1 + 0.6128 - (-2 + 0.1139) N = 1.9365 - 1 + 0.6128 + 2 - 0.1139 N = (1 - 1 + 2) + (0.9365 + 0.6128 - 0.1139) N = 2 + 1.4354 N = 3.4354 Step 5: Find the antilogarithm of 3.4354. N = antilog(3.4354) N = 10^3.4354 N ≈ 2725 The evaluated value is 2725. 12. Evaluate the following logarithms a) 3.892 × 2 Step 1: Rewrite the logarithmic expression using its characteristic and mantissa. 3.892 × 2 = (-3 + 0.892) × 2 Step 2: Distribute the multiplication. = (-3 × 2) + (0.892 × 2) = -6 + 1.784 Step 3: Convert back to characteristic/mantissa form. = -6 + 1 + 0.784 = -5 + 0.784 = 5.784 The evaluated logarithm is 5.784. b) 2.106 ÷ 2 Step 1: Rewrite the logarithmic expression using its characteristic and mantissa. 2.106 ÷ 2 = (-2 + 0.106) ÷ 2 Step 2: Distribute the division. = (-2)/(2) + (0.106)/(2) = -1 + 0.053 Step 3: Convert back to characteristic/mantissa form. = 1.053 The evaluated logarithm is 1.053. Send me the next one 📸