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: Convert all logarithms to a common base, which is base 2. We use the change of base formula: _b a = (_c a)/(_c b). For _4 x: _4 x = (_2 x)/(_2 4) = (_2 x)/(2) For _16 x: _16 x = (_2 x)/(_2 16) = (_2 x)/(4) Step 2: Substitute these expressions back into the original equation. _2 x + (_2 x)/(2) + (_2 x)/(4) = (21)/(4) Step 3: Let y = _2 x to simplify the equation. y + (y)/(2) + (y)/(4) = (21)/(4) Step 4: Combine the terms on the left side by finding a common denominator, which is 4. (4y)/(4) + (2y)/(4) + (y)/(4) = (21)/(4) (4y + 2y + y)/(4) = (21)/(4) (7y)/(4) = (21)/(4) Step 5: Solve for y. Multiply both sides by 4: 7y = 21 Divide by 7: y = (21)/(7) y = 3 Step 6: Substitute back y = _2 x and solve for x. _2 x = 3 By the definition of a logarithm, if _b a = c, then b^c = a. x = 2^3 x = 8 The final answer is 8. Send me the next one 📸