What is simplify-log_{10}(1.6*10^{-3}) ?

The solution to simplify-log_{10}(1.6*10^{-3}) is -log_{10}(1.6)+3

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simplify-log_{10}(1.6*10^{-3})

simplify

- lo g_{10} (1.6 \cdot 1 0^{- 3})

- lo g_{10} (1.6) + 3

Decimal Notation

2.79588 \dots

Solution steps

- lo g_{10} (1.6 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (1.6 \cdot 1 0^{- 3}) = lo g_{10} (1.6) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (1.6) + 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} (1.6) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (1.6) - 3)

Distribute parentheses

= - (lo g_{10} (1.6)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (1.6) + 3

- 2 ln (\frac{2}{2})

lo g_{10} (\frac{100}{x \cdot y ^{4}})

4 lo g_{10} (x) + lo g_{10} (y)

ln (4 x^{2} - 3) - ln (x^{2})

12 + 4 ln (\frac{9}{5})

What is simplify-log_{10}(1.6*10^{-3}) ?
The solution to simplify-log_{10}(1.6*10^{-3}) is -log_{10}(1.6)+3