An interesting thing about percentage change in GDP is it's worse on the downside than the upside. If GDP falls 40% one year, then rises 40% next year, it's not back at 100% of what it was before, it's actually only back to 84% (1.4 * 0.6).
We could choose the base to be ~2.7048138 such that 1% regular growth corresponds to 1% logarithmic growth. For low percentages they would mostly agree. But +40% would become +34% while -40% would become -51%, thus making the combined effect more apparent.