Answer:
In the given exponential equation \(2^{ax-3} = 128\), if the solution is \(x = 2\), you can substitute this value into the equation:
\[2^{a(2)-3} = 128\]
Simplify the exponent:
\[2^{2a-3} = 128\]
Now, since \(128 = 2^7\), you can express the equation as:
\[2^{2a-3} = 2^7\]
For these bases to be equal, the exponents must be equal:
\[2a-3 = 7\]
Now, solve for \(a\):
\[2a = 10\]
\[a = 5\]
Therefore, the coefficient of \(x\) is \(a = 5\).
