I am trying to utilise some AVX intrinsics in my code and have run into a brick wall with the logarithm intrinsics.
Using the Intel Intrinsics Guide v3.0.1 for Linux
As indicated in the comments to your question, that intrinsic doesn't map to an actual AVX instruction; it is an Intel extension to the intrinsic set. The implementation likely uses many underlying instructions, as a logarithm isn't a trivial operation.
If you'd like to use a non-Intel compiler but want a fast logarithm implementation, you might check out this open-source implementation of sin(), cos(), exp(), and log() functions using AVX. They are based on an earlier SSE2 version of the same functions.
I've posted my implementation of _mm256_log_pd(__m256d) here: https://stackoverflow.com/a/45898937/1915854 . With some effort you should be able to extend it to 8 packed floats instead of 4 doubles, though you need to revise the bit manipulations. And some parts are easies because you don't need to repack odd-/even-numbered 32-bit components of __m256i into __m128i.