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Popular >

simplify ln(2*10^{-2})

Solution

simplify

ln (2 \cdot 1 0^{- 2})

Solution

ln (2) - 2 ln (10)

+1

Decimal Notation

- 3.91202 \dots

Solution steps

ln (2 \cdot 1 0^{- 2})

Apply log rule:

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

ln (2 \cdot 1 0^{- 2}) = ln (2) + ln (1 0^{- 2})

= ln (2) + ln (1 0^{- 2})

Apply log rule:

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

ln (1 0^{- 2}) = - 2 ln (10)

= ln (2) - 2 ln (10)

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Frequently Asked Questions (FAQ)

What is ln(2*10^{-2}) ?
The solution to ln(2*10^{-2}) is ln(2)-2ln(10)