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\log_{10}\left(10^{-6}\right)
To multiply powers of the same base, add their exponents. Add 1 and -7 to get -6.
\log_{10}\left(\frac{1}{1000000}\right)
Calculate 10 to the power of -6 and get \frac{1}{1000000}.
-6
The base 10 logarithm of \frac{1}{1000000} is -6.