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: Take the natural logarithm of both sides of the inequality. Since the base 1.08 > 1, the inequality sign remains the same. ((1.08)^n+1) > (3) Step 2: Use the logarithm property (a^b) = b (a) to bring the exponent down. (n+1) (1.08) > (3) Step 3: Divide both sides by (1.08). Since 1.08 > 1, (1.08) is positive, so the inequality sign remains the same. n+1 > ((3))/((1.08)) Step 4: Calculate the numerical values of the logarithms. (3) ≈ 1.0986 (1.08) ≈ 0.07696 n+1 > (1.0986)/(0.07696) n+1 > 14.2749 Step 5: Subtract 1 from both sides to solve for n. n > 14.2749 - 1 n > 13.2749 The solution for n is: n > 13.2749