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
Here is the solution to problem 24: 24) (-3x - 1) - 7 = 2 Step 1: Use the logarithm property a - b = (a)/(b) to combine the terms on the left side. ((-3x-1)/(7)) = 2 Step 2: Convert the logarithmic equation to an exponential equation. Recall that y = x is equivalent to y = e^x. (-3x-1)/(7) = e^2 Step 3: Multiply both sides by 7. -3x-1 = 7e^2 Step 4: Add 1 to both sides. -3x = 7e^2 + 1 Step 5: Divide by -3 to solve for x. x = (7e^2 + 1)/(-3) x = -(7e^2 + 1)/(3) Step 6: Check the domain. The argument of the logarithm, -3x-1, must be greater than 0. Substitute the value of x: -3(-(7e^2 + 1)/(3)) - 1 = (7e^2 + 1) - 1 = 7e^2 Since e^2 is positive, 7e^2 is positive. Thus, the solution is valid. The exact answer is: x = -(7e^2 + 1)/(3)