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: Express the given expression in logarithmic form. Let X = sqrt((14.70 35^ 24')/(69.85^2)). First, convert 35^ 24' to decimal degrees: 35^ 24' = 35^ + (24)/(60)^ = 35^ + 0.4^ = 35.4^ So, the expression becomes: X = ((14.70 35.4^)/(69.85^2))^1/2 Taking the base-10 logarithm of both sides: X = [ ((14.70 35.4^)/(69.85^2))^1/2 ] Using the logarithm property (a^b) = b a: X = (1)/(2) ((14.70 35.4^)/(69.85^2)) Using the logarithm properties ((a)/(b)) = a - b and (ab) = a + b: X = (1)/(2) [(14.70) + ( 35.4^) - (69.85^2)] Using the logarithm property (a^b) = b a again: X = (1)/(2) [(14.70) + ( 35.4^) - 2 (69.85)] Step 2: Calculate the logarithms of the individual terms. Using a calculator for base-10 logarithms: (14.70) ≈ 1.1673173 First, calculate (35.4^): (35.4^) ≈ 0.7107090 Then, calculate its logarithm: ( 35.4^) = (0.7107090) ≈ -0.1483864 (69.85) ≈ 1.8441530 Step 3: Substitute these values into the equation for X. X = (1)/(2) [1.1673173 + (-0.1483864) - 2(1.8441530)] X = (1)/(2) [1.1673173 - 0.1483864 - 3.6883060] X = (1)/(2) [1.0189