Why regression models use log or exponential value?

I am not very familiar with statistic. Any statistician can help me to clarify what the difference are between exponential value and log value. I found in academic papers that regression models are usually shown in exponential value or log value.

1) what is the difference between them?
2) why most regression model use these values instead of absolute values?
3) How to calculate these values from absolute values? Or how to calculate absolute from those values also?

Thanks in advance.