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Popular >

simplify log_{10}(4*10^{-3})

Solution

simplify

lo g_{10} (4 \cdot 1 0^{- 3})

Solution

2 lo g_{10} (2) - 3

+1

Decimal Notation

- 2.39794 \dots

Solution steps

lo g_{10} (4 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (4 \cdot 1 0^{- 3}) = lo g_{10} (4) + lo g_{10} (1 0^{- 3})

= lo g_{10} (4) + lo g_{10} (1 0^{- 3})

Apply log rule:

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

lo g_{10} (1 0^{- 3}) = - 3 lo g_{10} (10)

= lo g_{10} (4) - 3 lo g_{10} (10)

3 lo g_{10} (10) = 3

= lo g_{10} (4) - 3

lo g_{10} (4) = 2 lo g_{10} (2)

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

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Frequently Asked Questions (FAQ)

What is log_{10}(4*10^{-3}) ?
The solution to log_{10}(4*10^{-3}) is 2log_{10}(2)-3