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
Hey Awesome, good to see you again. Step 1: Rewrite the first term using the exponent rule a^m-n = (a^m)/(a^n). 3^x-1 + 3^x = 36 (3^x)/(3^1) + 3^x = 36 Step 2: Factor out 3^x from the terms on the left side. 3^x ((1)/(3) + 1) = 36 Step 3: Simplify the expression inside the parentheses. 3^x ((1)/(3) + (3)/(3)) = 36 3^x ((4)/(3)) = 36 Step 4: Isolate 3^x by multiplying both sides by the reciprocal of (4)/(3), which is (3)/(4). 3^x = 36 × (3)/(4) 3^x = (108)/(4) 3^x = 27 Step 5: Express 27 as a power of 3. 3^x = 3^3 Step 6: Since the bases are the same, equate the exponents to solve for x. x = 3 The solution is x=3. Send me the next one 📸