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
Rofeehat, let's knock this out. Step 1: Apply the logarithm power rule, a b = (b^a), to the term x 4. 6 + (4^x) = 4 + (32 + 4^x) Step 2: Apply the logarithm product rule, a + b = (ab), to both sides of the equation. (6 · 4^x) = (4 · (32 + 4^x)) Step 3: Since the logarithms on both sides are equal, their arguments must be equal. 6 · 4^x = 4 · (32 + 4^x) Step 4: Let y = 4^x to simplify the equation and solve for y. 6y = 4(32 + y) 6y = 128 + 4y Subtract 4y from both sides: 6y - 4y = 128 2y = 128 Divide by 2: y = (128)/(2) y = 64 Step 5: Substitute y = 4^x back into the equation and solve for x. 4^x = 64 Recognize that 64 can be expressed as a power of 4: 64 = 4^3. 4^x = 4^3 Since the bases are the same, the exponents must be equal. x = 3 The final answer is 3. Send me the next one 📸