![Solve the following equations: b) 5^x - 6 imes 5^x+1 + 125 = 0. [Also, 3^x imes 5^x imes 7^x = 11,0252x+ is incomplete]](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1777187159064-6cdbb8652ec12bd7.png&w=3840&q=75)
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
Here are the solutions for the equations: 8. Solve each of the following equations b) 5^x - 6 × 5^x+1 + 125 = 0 Step 1: Use the exponent rule a^m+n = a^m × a^n to rewrite 5^x+1. 5^x+1 = 5^x × 5^1 = 5 × 5^x Step 2: Substitute this back into the equation. 5^x - 6 × (5 × 5^x) + 125 = 0 5^x - 30 × 5^x + 125 = 0 Step 3: Combine the terms involving 5^x. (1 - 30) × 5^x + 125 = 0 -29 × 5^x + 125 = 0 Step 4: Isolate the term with 5^x. -29 × 5^x = -125 5^x = (-125)/(-29) 5^x = (125)/(29) Step 5: Solve for x using logarithms. x = _5((125)/(29)) Step 6: Apply the logarithm property _b((M)/(N)) = _b(M) - _b(N). x = _5(125) - _5(29) Step 7: Simplify _5(125) since 125 = 5^3. x = 3 - _5(29) x = 3 - _5(29) The second equation, 3^x × 5^x × 7^x = 11,025^2x+, is incomplete as the exponent on the right side is cut off. Please provide the full equation for me to solve it. That's 2 down. 3 left today — send the next one.