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Popular >

simplify ln(9e^2)+ln(3e^{-2})

Solution

simplify

ln (9 e^{2}) + ln (3 e^{- 2})

Solution

3 ln (3)

+1

Decimal Notation

3.29583 \dots

Solution steps

ln (9 e^{2}) + ln (3 e^{- 2})

Apply log rule:

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

ln (9 e^{2}) + ln (3 e^{- 2}) = ln (9 \cdot 3 e^{- 2} e^{2})

= ln (9 \cdot 3 e^{- 2} e^{2})

9 e^{2} \cdot 3 e^{- 2} = 27

= ln (27)

Rewrite

27

in power-base form:

27 = 3^{3}

= ln (3^{3})

Apply log rule:

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

ln (3^{3}) = 3 ln (3)

= 3 ln (3)

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Frequently Asked Questions (FAQ)

What is ln(9e^2)+ln(3e^{-2}) ?
The solution to ln(9e^2)+ln(3e^{-2}) is 3ln(3)