What is simplify-log_{10}(3.8*10^{-3}) ?

The solution to simplify-log_{10}(3.8*10^{-3}) is -log_{10}(3.8)+3

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simplify-log_{10}(3.8*10^{-3})

simplify

- lo g_{10} (3.8 \cdot 1 0^{- 3})

- lo g_{10} (3.8) + 3

Decimal Notation

2.42021 \dots

Solution steps

- lo g_{10} (3.8 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (3.8 \cdot 1 0^{- 3}) = lo g_{10} (3.8) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (3.8) + 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} (3.8) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (3.8) - 3)

Distribute parentheses

= - (lo g_{10} (3.8)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (3.8) + 3

\frac{ln ( 10 )}{2 ln ( 2 ) - ln ( 5 )}

\frac{9}{10} ln (30)

- \frac{9}{20} \cdot lo g_{2} (\frac{9}{20}) - \frac{1}{20} \cdot lo g_{2} (\frac{1}{20})

\frac{3 ln ( 20 )}{2 ln ( 19 ) - ln ( 20 )}

What is simplify-log_{10}(3.8*10^{-3}) ?
The solution to simplify-log_{10}(3.8*10^{-3}) is -log_{10}(3.8)+3