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Popular >

simplify ln(1*10^{-3})

Solution

simplify

ln (1 \cdot 1 0^{- 3})

Solution

- 3 ln (10)

+1

Decimal Notation

- 6.90775 \dots

Solution steps

ln (1 \cdot 1 0^{- 3})

Apply log rule:

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

ln (1 \cdot 1 0^{- 3}) = ln (1) + ln (1 0^{- 3})

= ln (1) + ln (1 0^{- 3})

Apply log rule:

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

ln (1 0^{- 3}) = - 3 ln (10)

= ln (1) - 3 ln (10)

Apply log rule:

lo g_{a} (1) = 0

= 0 - 3 ln (10)

0 - 3 ln (10) = - 3 ln (10)

= - 3 ln (10)

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Frequently Asked Questions (FAQ)

What is ln(1*10^{-3}) ?
The solution to ln(1*10^{-3}) is -3ln(10)