kayleebug77777 kayleebug77777
  • 24-01-2024
  • Mathematics
contestada

Consider the exponential equation.
2^(ax-3) = 128
If the solution to the equation is x = 2, what is the coefficient of x?

Respuesta :

Meherpuya
Meherpuya Meherpuya
  • 24-01-2024

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 \(a = 5\).

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