Example Question - base

Solving an Exponential Equation

The equation in the image is: \(2^{3x+5} = 2^{1-x}\) To solve for \(x\), since the bases are the same, you can set the exponents equal to each other: \(3x + 5 = 1 - x\) Now, solve for \(x\): Add \(x\) to both sides: \(3x + x + 5 = 1 - x + x\) \(4x + 5 = 1\) Subtract 5 from both sides: \(4x + 5 - 5 = 1 - 5\) \(4x = -4\) Divide both sides by 4: \(x = -4 / 4\) \(x = -1\)