What is simplify-log_{10}(4\times 10^{-4}) ?

The solution to simplify-log_{10}(4\times 10^{-4}) is -2log_{10}(2)+4

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simplify-log_{10}(4\times 10^{-4})

simplify

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

- 2 lo g_{10} (2) + 4

Decimal Notation

3.39794 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

4 lo g_{10} (10) = 4

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

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

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

Distribute parentheses

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

Apply minus-plus rules

- (- a) = a, - (a) = - a

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

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What is simplify-log_{10}(4\times 10^{-4}) ?
The solution to simplify-log_{10}(4\times 10^{-4}) is -2log_{10}(2)+4