You should replace the EPS with a PDF/X-4 and inform your client that EPS is an outdated old file type. At least you should add the PDF/X-4 and make your client learn that he should pass on the PDF.
A JPG for a logo is never a good idea. For professional purposes you will use the PDF/X-4, if someone needs for non professional programs a rasterized image he should use PNG.
JPG makes artifacts wich are very visible in smooth areas and therefor JPG is the wrong file type for logos, JPG does also not support transparency, PNG could do it on PPTX slides or in Word documents.