I am not sure if this is helpful but I hope it will be.
Is the text you are using in "text format" or "shape format" meaning, can u type in and change it or are they like shapes so its not "editable" to type in? Thing is, they can be in vector "shapes" and this sometimes will 'cause the points to move around when you are changing the size. I would suggest that if it is possible, for you to type it in again using that font and choosing directly the font size you need (Character Tool: command+C [Mac). If it is within a logo and its hard for you to retype it then maybe you can keep it as is with the size but when exporting you can change the size of the element.
ie: Follow what I am trying to explain. Go to File>Save for Web. You will get a pop-up, on the side there is an option called "Image Size" write in the size you want and just use it from there..
If you fell the Illustrator technique doesnt work, you can try with photoshop. Open a new file with the dimensions you want. Drag the file that you have of the logo or text into the page area. Make sure you have the Layer's tools on the side showing (Windows>Layers). Check if you have on the layer of your logo/text a small "page" icon that means it is a "Smart Object", this will make it safe to resize. From there you can just save it to whatever format you need using File>Save As...
I hope that was helpful, honestly its not as complicated as it might sound, just try going step by step with what I gave you.. :)