What is log_{10}(8*10^{-7}) ?

The solution to log_{10}(8*10^{-7}) is 3log_{10}(2)-7

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simplify log_{10}(8*10^{-7})

simplify

lo g_{10} (8 \cdot 1 0^{- 7})

3 lo g_{10} (2) - 7

Solution steps

lo g_{10} (8 \cdot 1 0^{- 7})

Apply log rule:

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

lo g_{10} (8 \cdot 1 0^{- 7}) = lo g_{10} (8) + lo g_{10} (1 0^{- 7})

= lo g_{10} (8) + lo g_{10} (1 0^{- 7})

Apply log rule:

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

lo g_{10} (1 0^{- 7}) = - 7 lo g_{10} (10)

= lo g_{10} (8) - 7 lo g_{10} (10)

7 lo g_{10} (10) = 7

= lo g_{10} (8) - 7

lo g_{10} (8) = 3 lo g_{10} (2)

= 3 lo g_{10} (2) - 7

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What is log_{10}(8*10^{-7}) ?
The solution to log_{10}(8*10^{-7}) is 3log_{10}(2)-7