Logarithmic and exponential functions play an important role in complex analysis. There are many areas in complex analysis where logarithmic and exponential functions are used. Infinite product is one of them. In this research paper, we will discuss important results of Infinite products with logarithmic and exponential functions. Exponential and logarithmic functions are very important when we discuss them in an infinite product, because they give us many useful results with infinite product. We will discuss a very important relation of logarithmic and exponential function in an infinite product.