What is simplify-log_{10}(1.89*10^{-3}) ?

The solution to simplify-log_{10}(1.89*10^{-3}) is -log_{10}(1.89)+3

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simplify-log_{10}(1.89*10^{-3})

simplify

- lo g_{10} (1.89 \cdot 1 0^{- 3})

- lo g_{10} (1.89) + 3

Decimal Notation

2.72353 \dots

Solution steps

- lo g_{10} (1.89 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (1.89 \cdot 1 0^{- 3}) = lo g_{10} (1.89) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (1.89) + 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} (1.89) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (1.89) - 3)

Distribute parentheses

= - (lo g_{10} (1.89)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (1.89) + 3

ln (\frac{30}{42})

0.25 ln (2) + 1.75 ln (3) + 5.5 ln (2)

24 (136 ln^{2} (7) - 4 ln^{2} (5))

6.1 + lo g_{10} (\frac{24}{( 0.03 \cdot 30 )})

ln (\frac{x ^{2} + y ^{2} \cdot 2 + arctan ( \frac{y}{x} )}{2})

What is simplify-log_{10}(1.89*10^{-3}) ?
The solution to simplify-log_{10}(1.89*10^{-3}) is -log_{10}(1.89)+3