Frequency scaling of audio signals

I have an audio signal x[n], whose frequency varies over time. It's FT is X[k]. I want to reconstruct an audio signal (x_hat[n]) from X[k] such that, at any given time:

frequency_of_x_hat[n] = log10(frequency_of_x[n])

i.e. the frequencies are compressed logarithmically. Any idea about how to do this? Thanks.

[KALYAN ACHARJYA]

Then what the problem, implement the statement in the code.

[Shoaibur Rahman]

Thanks, Kalyan! I don't know how to implement it. Let's consider the following signal:

% Load a signal y and it's sampling frequency Fs
load('chirp.mat')
x = y;
x_hat = ????

How would you do this?