What is simplify-log_{10}(8.41*10^{-4}) ?

The solution to simplify-log_{10}(8.41*10^{-4}) is -log_{10}(8.41)+4

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simplify-log_{10}(8.41*10^{-4})

simplify

- lo g_{10} (8.41 \cdot 1 0^{- 4})

- lo g_{10} (8.41) + 4

Decimal Notation

3.07520 \dots

Solution steps

- lo g_{10} (8.41 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (8.41 \cdot 1 0^{- 4}) = lo g_{10} (8.41) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (8.41) + lo g_{10} (1 0^{- 4}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (1 0^{- 4}) = - 4 lo g_{10} (10)

= - (lo g_{10} (8.41) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (8.41) - 4)

Distribute parentheses

= - (lo g_{10} (8.41)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (8.41) + 4

ln (\frac{p}{x})

lo g_{10} (\frac{x ^{3} y}{x ^{3}})

- ln \frac{1}{2} + 1 + ln \frac{1}{2} + 1 + 1 + ln (3)

5 \cdot ln (x^{3}) - ln (x^{2})

- lo g_{10} (1 0^{- 14} \frac{1}{4.4 \cdot 1 0 ^{- 4}})

What is simplify-log_{10}(8.41*10^{-4}) ?
The solution to simplify-log_{10}(8.41*10^{-4}) is -log_{10}(8.41)+4