What is 3/(sqrt(41))ln(2e) ?

The solution to 3/(sqrt(41))ln(2e) is (sqrt(41)(3ln(2)+3))/(41)

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simplify 3/(sqrt(41))ln(2e)

simplify

\frac{3}{41} ln (2 e)

\frac{41 ( 3 ln ( 2 ) + 3 )}{41}

Decimal Notation

0.79327 \dots

Solution steps

\frac{3}{41} ln (2 e)

Apply log rule:

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

\frac{3}{41} ln (2 e) = \frac{3}{41} ln (2) + \frac{3}{41} ln (e)

= \frac{3}{41} ln (2) + \frac{3}{41} ln (e)

\frac{3}{41} ln (e) = \frac{3}{41}

= \frac{3}{41} ln (2) + \frac{3}{41}

Multiply

\frac{3}{41} ln (2) : \frac{3 ln ( 2 )}{41}

= \frac{3 ln ( 2 )}{41} + \frac{3}{41}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 ln ( 2 ) + 3}{41}

Rationalize

\frac{3 ln ( 2 ) + 3}{41} : \frac{41 ( 3 ln ( 2 ) + 3 )}{41}

= \frac{41 ( 3 ln ( 2 ) + 3 )}{41}

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

\frac{1}{2} ln (x) - 5 ln (y) + 4 ln (z)

2 ln (a) - ln (3 b) + 2 ln (2)

lo g_{10} (3 x) - 1

lo g_{b} (19 x^{5} y)

What is 3/(sqrt(41))ln(2e) ?
The solution to 3/(sqrt(41))ln(2e) is (sqrt(41)(3ln(2)+3))/(41)