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The difference between the points 0.0000000398 and 0.00000000398 relates to the concept of logarithms, which help in understanding both small and large numbers. Logarithms express numbers as exponents of a base. For instance, in the exponential equation where base \( b \) is raised to power \( p \), it equals a number \( n \). The exponent \( p \) represents the logarithm of \( n \). For example, the logarithm base 10 of 10,000 can be determined by asking what power 10 must be raised to in order to equal 10,000. Since \( 10^4 = 10,000 \), this means that \( \log_{10}(10,000) = 4 \). This concept is essential for explaining numerical differences as well as the phenomena like red eyes after swimming.
