What is ln(2e)*3/(sqrt(59)) ?

The solution to ln(2e)*3/(sqrt(59)) is (sqrt(59)(3ln(2)+3))/(59)

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simplify ln(2e)*3/(sqrt(59))

simplify

ln (2 e) \cdot \frac{3}{59}

\frac{59 ( 3 ln ( 2 ) + 3 )}{59}

Decimal Notation

0.66128 \dots

Solution steps

ln (2 e) \frac{3}{59}

Apply log rule:

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

ln (2 e) \frac{3}{59} = \frac{3}{59} ln (2) + \frac{3}{59} ln (e)

= \frac{3}{59} ln (2) + \frac{3}{59} ln (e)

\frac{3}{59} ln (e) = \frac{3}{59}

= \frac{3}{59} ln (2) + \frac{3}{59}

Multiply

\frac{3}{59} ln (2) : \frac{3 ln ( 2 )}{59}

= \frac{3 ln ( 2 )}{59} + \frac{3}{59}

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}{59}

Rationalize

\frac{3 ln ( 2 ) + 3}{59} : \frac{59 ( 3 ln ( 2 ) + 3 )}{59}

= \frac{59 ( 3 ln ( 2 ) + 3 )}{59}

lo g_{10} (8) + lo g_{10} (5) + lo g_{10} (3)

lo g_{6} (36 x^{3})

lo g_{10} (\frac{1}{2} x)

ln^{2} (x) - ln^{2} (y)

What is ln(2e)*3/(sqrt(59)) ?
The solution to ln(2e)*3/(sqrt(59)) is (sqrt(59)(3ln(2)+3))/(59)