What is (1/(sqrt(e)))^2log_{3}(1/(sqrt(e))) ?

The solution to (1/(sqrt(e)))^2log_{3}(1/(sqrt(e))) is -1/(2e)log_{3}(e)

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simplify (1/(sqrt(e)))^2log_{3}(1/(sqrt(e)))

simplify

(\frac{1}{e})^{2} lo g_{3} (\frac{1}{e})

- \frac{1}{2 e} lo g_{3} (e)

Decimal Notation

- 0.16742 \dots

Solution steps

(\frac{1}{e})^{2} lo g_{3} (\frac{1}{e})

Apply log rule:

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

lo g_{3} (\frac{1}{e}) = lo g_{3} (1) - lo g_{3} (e)

= (\frac{1}{e})^{2} (lo g_{3} (1) - lo g_{3} (e))

(\frac{1}{e})^{2} = \frac{1}{e}

= \frac{1}{e} (lo g_{3} (1) - lo g_{3} (e))

lo g_{3} (1) = 0

lo g_{3} (e) = \frac{1}{2} lo g_{3} (e)

= \frac{1}{e} (- \frac{1}{2} lo g_{3} (e) + 0)

0 - \frac{1}{2} lo g_{3} (e) = - \frac{1}{2} lo g_{3} (e)

= \frac{1}{e} (- \frac{1}{2} lo g_{3} (e))

Remove parentheses:

(- a) = - a

= - \frac{1}{e} \cdot \frac{1}{2} lo g_{3} (e)

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= - \frac{1 \cdot 1}{2 e} lo g_{3} (e)

Multiply the numbers:

1 \cdot 1 = 1

= - \frac{1}{2 e} lo g_{3} (e)

4 lo g_{10} (3) + 1 lo g_{10} (x)

lo g_{4} (\frac{x ^{2} y}{z})

lo g_{10} (x) - 5 lo g_{10} (y) + 6 lo g_{10} (z)

\frac{1}{4} lo g_{b} (x) + 2 lo g_{b} (y) - 3 lo g_{b} (x)

ln (8 x + 4) - 2 ln (2)

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