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Popular >

simplify ln((e^3)/9)

Solution

simplify

ln (\frac{e ^{3}}{9})

Solution

3 - 2 ln (3)

+1

Decimal Notation

0.80277 \dots

Solution steps

ln (\frac{e ^{3}}{9})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

= ln (e^{3}) - ln (9)

Apply log rule:

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

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

= 3 ln (e) - ln (9)

3 ln (e) = 3

= 3 - ln (9)

ln (9) = 2 ln (3)

= 3 - 2 ln (3)

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Frequently Asked Questions (FAQ)

What is ln((e^3)/9) ?
The solution to ln((e^3)/9) is 3-2ln(3)