What is log_{10}(10^{-6}*20) ?

The solution to log_{10}(10^{-6}*20) is -6+log_{10}(20)

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simplify log_{10}(10^{-6}*20)

simplify

lo g_{10} (1 0^{- 6} \cdot 20)

- 6 + lo g_{10} (20)

Decimal Notation

- 4.69897 \dots

Solution steps

lo g_{10} (1 0^{- 6} \cdot 20)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (1 0^{- 6} \cdot 20) = lo g_{10} (1 0^{- 6}) + lo g_{10} (20)

= lo g_{10} (1 0^{- 6}) + lo g_{10} (20)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (1 0^{- 6}) = - 6 lo g_{10} (10)

= - 6 lo g_{10} (10) + lo g_{10} (20)

6 lo g_{10} (10) = 6

= - 6 + lo g_{10} (20)

3 ln (2) - 3 ln (2 + 1)

ln (\frac{a ^{2}}{b ^{- 3} c ^{2}})

ln (\frac{10000}{8600})

ln (x^{3}) + ln (y)

ln (\frac{1 + 8}{2 + 16})

What is log_{10}(10^{-6}*20) ?
The solution to log_{10}(10^{-6}*20) is -6+log_{10}(20)