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Popular >

simplify ln(8/(e^3))

Solution

simplify

ln (\frac{8}{e ^{3}})

Solution

3 ln (2) - 3

+1

Decimal Notation

- 0.92055 \dots

Solution steps

ln (\frac{8}{e ^{3}})

Apply log rule:

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

ln (\frac{8}{e ^{3}}) = ln (8) - ln (e^{3})

= ln (8) - ln (e^{3})

Apply log rule:

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

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

= ln (8) - 3 ln (e)

3 ln (e) = 3

= ln (8) - 3

ln (8) = 3 ln (2)

= 3 ln (2) - 3

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Frequently Asked Questions (FAQ)

What is ln(8/(e^3)) ?
The solution to ln(8/(e^3)) is 3ln(2)-3