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
Another one Ø+T — let's solve it. Here are the solutions to the problems: 1. 2^x = 2 Step 1: Rewrite the right side with the same base as the left side. 2^x = 2^1 Step 2: Since the bases are the same, equate the exponents. x = 1 The solution is x=1. 2. 5^2x+1 = 125 Step 1: Express 125 as a power of 5. 5^2x+1 = 5^3 Step 2: Since the bases are the same, equate the exponents. 2x+1 = 3 Step 3: Solve the linear equation for x. 2x = 3 - 1 2x = 2 x = (2)/(2) x = 1 The solution is x=1. 3. x^3 = 64 Step 1: Express 64 as a cube of an integer. x^3 = 4^3 Step 2: Take the cube root of both sides. x = 4 The solution is x=4. 4. 2(3^x) = 18 Step 1: Divide both sides by 2. (2(3^x))/(2) = (18)/(2) 3^x = 9 Step 2: Express 9 as a power of 3. 3^x = 3^2 Step 3: Since the bases are the same, equate the exponents. x = 2 The solution is x=2. 5. 3 × 5^2x+4 = 75 Step 1: Divide both sides by 3. 3 × 5^2x+43 = (75)/(3) 5^2x+4 = 25 Step 2: Express 25 as a power of 5. 5^2x+4 = 5^2 Step 3: Since the bases are the same, equate the exponents. 2x+4 = 2 Step 4: Solve the linear equation for x. 2x = 2 - 4 2x = -2 x = (-2)/(2) x = -1 The solution is x=-1. Send me the next one 📸