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Popular >

simplify log_{10}(5*10^{-3})

Solution

simplify

lo g_{10} (5 \cdot 1 0^{- 3})

Solution

lo g_{10} (5) - 3

+1

Decimal

- 2.30102 \dots

Solution steps

lo g_{10} (5 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (5 \cdot 1 0^{- 3}) = lo g_{10} (5) + lo g_{10} (1 0^{- 3})

= lo g_{10} (5) + 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} (5) - 3 lo g_{10} (10)

3 lo g_{10} (10) = 3

= lo g_{10} (5) - 3

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Frequently Asked Questions (FAQ)

What is log_{10}(5*10^{-3}) ?
The solution to log_{10}(5*10^{-3}) is log_{10}(5)-3