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The base 10 logarithm is called the _____ logarithm and is often written as log x instead of log10 x.,

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A common logarithm is any logarithm with base 10. Our number system is base 10; there are ten digits from 0-9, and place value is determined by groups of ten. You can remember a “common logarithm,” then, as any logarithm whose base is our “common” base, 10.
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