Alī Muḥammad Iṣfahānī (1215/1800–1293/1876), was one of the famous scientific figures of Qajar period who passed the formative years of his scientific and professional life in Iṣfahān, i.e. before being acquainted with the European sciences through the modern institution of Dār al-Funūn. Several scientific works of Iṣfahānī were written in the style of the ancient mathematical treatises like Miftāḥ al-Ḥisāb by Kāshī or ‘Uyūn al-Ḥisāb by Muḥammad Bāghir Yazdī, whereas his other works seem to have been written in the style of the pedagogic books of Dār al-Funūn. The historians have mentioned some titles among Iṣfahānī’s works which unfortunately are not available today and therefore the attribution of some innovations to Iṣfahānī remains ambiguous. One of the innovations attributed to Iṣfahānī is the discovery of the extracting the LOGARITHM of the numbers. This attribution is repeated in some historical Persian sources such as The Diffused Articles by Abu al-Ḥasan Furūghī, The Algebra of Khayyām by Gholamhossein Mosaheb, The History of Islamic Sciences by Jalal al-Din Homaee, etc. Nevertheless, the historian of mathematics, Abu al-Ghasim Ghorbani, believes that the attribution of discovery of the LOGARITHM to Iṣfahānī could not be more than a legend, though after examining some historical facts, Abd al-Hossein Moshafi shows that this attribution is not far from reality. In this article, after introducing this mathematician and mentioning the previous debates about the subject, I will try to shed some light on these ambiguities with the help of the extant documents.