One of the advantages of the log link is that it stabilizes the variance of data with a constant coefficient of variation. By doing so, one could run ordinary least squares on the log-transformed data. However, your intercepts would be biased by the offset -0.5*$v$ where $v$ is the coefficient of variation. Restating what Gordon touched upon in the comments, links such as the sqrt link are often not justifiable. Even the canonical inverse link is not practical.
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