I know an MRI is better to show herniated discs will CT scan show the same thing?

NOT CLOSE. MRI is superior is showing not only disc itself but also disc fragments, and nerve root compression. CT better in looking for bone abnormalities such as fractures.
No. No not effectively. An MRI is required for appropriate detail unless if metal is present in the back in which case a CT myelogram may be necessary secondary to the "shadow" created by the metal.

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