If `3^(4x-2) = 729`, then find the value of `x`.
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If `3^(4x-2) = 729`, then find the value of `x`.
We have the equation \(3^{4x – 2} = 729\). We can rewrite 729 as a power of 3, since \(729 = 3^6\). Therefore, the equation becomes:
\[3^{4x – 2} = 3^6\]
Since the bases are the same, we can set the exponents equal to each other:
\[4x – 2 = 6\]
Solving for \(x\):
\[4x = 6 + 2\]
\[4x = 8\]
\[x = \frac{8}{4}\]
\[x = 2\]
So, the value of \(X\) is 2.