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: Express all numbers in the equation as powers of the same base. The base 2 is suitable. 2 = 2^1 8 = 2^3 128 = 2^7 Step 2: Substitute these into the given equation. 2^(x-3) × (2^3)^(x+2) = 2^7 Step 3: Apply the exponent rule (a^m)^n = a^mn to the term (2^3)^(x+2). 2^(x-3) × 2^3(x+2) = 2^7 2^(x-3) × 2^(3x+6) = 2^7 Step 4: Apply the exponent rule a^m × a^n = a^m+n to the left side of the equation. 2^(x-3) + (3x+6) = 2^7 2^(x+3x-3+6) = 2^7 2^(4x+3) = 2^7 Step 5: Since the bases are equal, equate the exponents. 4x+3 = 7 Step 6: Solve the linear equation for x. 4x = 7 - 3 4x = 4 x = (4)/(4) x = 1 The value of x is 1.