What is simplify-log_{10}(1.9*10^{-3}) ?

The solution to simplify-log_{10}(1.9*10^{-3}) is -log_{10}(1.9)+3

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simplify-log_{10}(1.9*10^{-3})

simplify

- lo g_{10} (1.9 \cdot 1 0^{- 3})

- lo g_{10} (1.9) + 3

Decimal

2.72124 \dots

Solution steps

- lo g_{10} (1.9 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (1.9 \cdot 1 0^{- 3}) = lo g_{10} (1.9) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (1.9) + 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} (1.9) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (1.9) - 3)

Distribute parentheses

= - (lo g_{10} (1.9)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (1.9) + 3

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

ln (\frac{1}{x ^{2} + y ^{2}})

\frac{8.314 \cdot 310}{1 \cdot 96485} ln (\frac{5.3}{140})

lo g_{10} (x + 2) - \frac{1}{2} lo g_{10} (1 + x^{2})

5 lo g_{a} (a) - lo g_{a} (a^{7}) + lo g_{a} (a^{- 3})

What is simplify-log_{10}(1.9*10^{-3}) ?
The solution to simplify-log_{10}(1.9*10^{-3}) is -log_{10}(1.9)+3