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Popular >

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

Solution

simplify

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

Solution

ln (3) - 3 ln (10)

+1

Decimal Notation

- 5.80914 \dots

Solution steps

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

Apply log rule:

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

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

= ln (3) + 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 (3) - 3 ln (10)

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Frequently Asked Questions (FAQ)

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