Logarithmic multiplication simplifies the process of multiplication for numbers with large dynamic range values by adding them, enabling efficient and high-precision computations. In the real world, algorithms employed in digital signal processing frequently include several multiplications, which can be time- and energy-intensive, and logarithmic multipliers are employed in audio processing, particularly in audio compression and equalization. Logarithmic multipliers are sometimes preferred over conventional multipliers since they provide benefits in dynamic range, precision, and computational efficiency. Mitchell's algorithm is a prominent approach to logarithmic multiplication that simplifies the process by converting multiplication operations into addition operations in logarithmic space. This paper explores and implements logarithmic multiplication methodology in multiplication techniques. The primary focus lies on the Iterative Logarithmic Multiplier, its pipeline variant with error correction to achieve more efficient and versatile multiplication processes implemented using Verilog HDL. The proposed pipeline logarithmic multipliers consume less power than the iterative logarithmic multipliers by almost 70%. Even though the pipeline implementation consumes less power than the iterative approach, it consumes more time, almost thrice.