What is simplify-log_{10}(4\times 10^{-3}) ?

The solution to simplify-log_{10}(4\times 10^{-3}) is -2log_{10}(2)+3

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simplify-log_{10}(4\times 10^{-3})

simplify

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

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

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)

Distribute parentheses

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

Apply minus-plus rules

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

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

ln (3 x)

ln (x (x + 4) (x + 5))

ln (5) + 4 ln (x) - 8 ln (y)

lo g_{5} (5 x^{- 5})

3 ln (x) + 4 ln (y) - 2 ln (z)

What is simplify-log_{10}(4\times 10^{-3}) ?
The solution to simplify-log_{10}(4\times 10^{-3}) is -2log_{10}(2)+3