What is simplify-log_{10}(2.19*10^{-3}) ?

The solution to simplify-log_{10}(2.19*10^{-3}) is -log_{10}(2.19)+3

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simplify-log_{10}(2.19*10^{-3})

simplify

- lo g_{10} (2.19 \cdot 1 0^{- 3})

- lo g_{10} (2.19) + 3

Decimal Notation

2.65955 \dots

Solution steps

- lo g_{10} (2.19 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (2.19 \cdot 1 0^{- 3}) = lo g_{10} (2.19) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (2.19) + 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} (2.19) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (2.19) - 3)

Distribute parentheses

= - (lo g_{10} (2.19)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (2.19) + 3

\frac{1}{1.212855959 \cdot 1 0 ^{- 4}} ln (\frac{100}{23})

e^{((l n (x) - l n (θ)) (m - 1))}

\frac{1}{4} ln (\frac{14}{5})

\frac{1}{4} lo g_{10} (3)

ln (\frac{x ^{4}}{4})

What is simplify-log_{10}(2.19*10^{-3}) ?
The solution to simplify-log_{10}(2.19*10^{-3}) is -log_{10}(2.19)+3