Question

solve the equation. $2^{(3x - 5)} = 128$ (20 points)
x = \square

Explanation:

Step1: Express 128 as a power of 2

We know that \(128 = 2^7\), so the equation \(2^{(3x - 5)}=128\) can be rewritten as \(2^{(3x - 5)} = 2^7\).

Step2: Set the exponents equal

Since the bases are the same (both are 2) and the equation holds, the exponents must be equal. So we have the equation \(3x - 5=7\).

Step3: Solve for x

First, add 5 to both sides of the equation: \(3x-5 + 5=7 + 5\), which simplifies to \(3x=12\). Then, divide both sides by 3: \(\frac{3x}{3}=\frac{12}{3}\), so \(x = 4\).

Answer:

\(4\)