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An image exported to JPEG or TIFF is always 72 dpi, regardless of the resolution set in the Export Options Dialog. However, the size of the image changes proportionally with changes to the resolution. For example, a 2" x 4" layout at 300 dpi actually creates an output image that is 8.33" x 16.67" at 72 dpi.
The JPEG and TIFF export drivers write 'unit-less' in the Resolution Unit entry of the image header. This means that the horizontal and vertical resolution entries are treated as a pixel aspect ratio rather than as a count of pixels per resolution unit. When an external application reads this entry in the header, it defaults to 72 dpi.
Make sure the image is not resampled when resizing. This will maintain the same total number of pixels in the new image, thus changing the image resolution. Depending on your graphics application this option may be referred to as 'Maintain original size', 'Resample Image', or 'Actual/Print Size'.