What is simplify-log_{10}(2\times 10^{-3}) ?

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

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simplify-log_{10}(2\times 10^{-3})

simplify

- lo g_{10} (2 \cdot 1 0^{- 3})

- lo g_{10} (2) + 3

Decimal Notation

2.69897 \dots

Solution steps

- lo g_{10} (2 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (2 \cdot 1 0^{- 3}) = lo g_{10} (2) + lo g_{10} (1 0^{- 3})

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

3 lo g_{10} (10) = 3

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

Distribute parentheses

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

Apply minus-plus rules

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

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

\frac{1}{2} lo g_{3} (8) + \frac{1}{2} lo g_{3} (18) - 1

lo g_{m} (a b^{2} c^{3})

- lo g_{10} (1.32 \cdot 1 0^{- 3})

lo g_{10} (10 a)

5 ln (x) - \frac{1}{5} ln (y)

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