Show that the system described by the equation 
in which x is the excitation and y is the response is non-linear, time invariant, BIBO stable, static, causal and invertible.
What will be an ideal response?
If x is bounded y is also bounded. Therefore the system is BIBO stable.
The response y at any time depends only on the excitation x at the same time. Therefore the system is static and causal.
ln (y[n] = x[n] Therefore knowledge of y allows determination of x and the system is invertible.
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What will be an ideal response?