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Popular >

simplify ln(1/(sqrt(e^3)))

Solution

simplify

ln (\frac{1}{e ^{3}})

Solution

- \frac{3}{2}

+1

Decimal Notation

- 1.5

Solution steps

ln (\frac{1}{e ^{3}})

\frac{1}{e ^{3}} = \frac{1}{e e}

= ln (\frac{1}{e e})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (e e)

Apply log rule:

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

ln (e e) = ln (e) + ln (e)

= - (ln (e) + ln (e))

Simplify

ln (e) : \frac{1}{2}

Apply log rule:

lo g_{a} (a) = 1

= - (\frac{1}{2} + 1)

Join

1 + \frac{1}{2} : \frac{3}{2}

= - \frac{3}{2}

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Frequently Asked Questions (FAQ)

What is ln(1/(sqrt(e^3))) ?
The solution to ln(1/(sqrt(e^3))) is -3/2