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
Step 1: Rewrite the logarithm with base 4 using the change of base formula. The change of base formula is _b a = (_c a)/(_c b). We will change _4 x to base 2. _4 x = (_2 x)/(_2 4) Since 2^2 = 4, we know that _2 4 = 2. _4 x = (_2 x)/(2) Step 2: Substitute this expression back into the original equation. _2 x + (_2 x)/(2) = 6 Step 3: Combine the terms involving _2 x. Let y = _2 x. y + (y)/(2) = 6 (2y)/(2) + (y)/(2) = 6 (3y)/(2) = 6 Step 4: Solve for y. Multiply both sides by 2: 3y = 12 Divide both sides by 3: y = 4 Step 5: Substitute back y = _2 x and solve for x. _2 x = 4 Convert the logarithmic equation to an exponential equation. If _b a = c, then b^c = a. x = 2^4 x = 16 The final answer is 16. Send me the next one 📸