What is ln(2e)(5/(sqrt(33))) ?

The solution to ln(2e)(5/(sqrt(33))) is (sqrt(33)(5ln(2)+5))/(33)

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simplify ln(2e)(5/(sqrt(33)))

simplify

ln (2 e) (\frac{5}{33})

\frac{33 ( 5 ln ( 2 ) + 5 )}{33}

Decimal Notation

1.47369 \dots

Solution steps

ln (2 e) (\frac{5}{33})

Apply log rule:

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

ln (2 e) (\frac{5}{33}) = (\frac{5}{33}) ln (2) + (\frac{5}{33}) ln (e)

= (\frac{5}{33}) ln (2) + (\frac{5}{33}) ln (e)

Remove parentheses:

(a) = a

= \frac{5}{33} ln (2) + \frac{5}{33} ln (e)

\frac{5}{33} ln (e) = \frac{5}{33}

= \frac{5}{33} ln (2) + \frac{5}{33}

Multiply

\frac{5}{33} ln (2) : \frac{5 ln ( 2 )}{33}

= \frac{5 ln ( 2 )}{33} + \frac{5}{33}

Since the denominators are equal, combine the fractions:

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

= \frac{5 ln ( 2 ) + 5}{33}

Rationalize

\frac{5 ln ( 2 ) + 5}{33} : \frac{33 ( 5 ln ( 2 ) + 5 )}{33}

= \frac{33 ( 5 ln ( 2 ) + 5 )}{33}

ln (3 e^{2 θ})

5 ln (3) + 5 ln (3) + 5 ln (2)

ln (m x)

ln (5.6 x^{7.8})

ln (\frac{0.15}{1.2})

What is ln(2e)(5/(sqrt(33))) ?
The solution to ln(2e)(5/(sqrt(33))) is (sqrt(33)(5ln(2)+5))/(33)