This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Step 1: Rewrite the terms with a common base. The equation is 49^x+1 + 7^2x = 350. Since 49 = 7^2, we can rewrite 49^x+1 as (7^2)^x+1. (7^2)^x+1 + 7^2x = 350 Step 2: Apply the exponent rule (a^m)^n = a^mn. 7^2(x+1) + 7^2x = 350 7^2x+2 + 7^2x = 350 Step 3: Apply the exponent rule a^m+n = a^m · a^n. 7^2x · 7^2 + 7^2x = 350 7^2x · 49 + 7^2x = 350 Step 4: Factor out the common term 7^2x. 7^2x(49 + 1) = 350 7^2x(50) = 350 Step 5: Isolate 7^2x. 7^2x = (350)/(50) 7^2x = 7 Step 6: Equate the exponents. Since 7 = 7^1, we can write: 7^2x = 7^1 For the equality to hold, the exponents must be equal. 2x = 1 Step 7: Solve for x. x = (1)/(2) The value of x is (1)/(2). Send me the next one 📸