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Popular >

simplify ln(2sqrt(2))

Solution

simplify

ln (22)

Solution

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

+1

Decimal Notation

1.03972 \dots

Solution steps

ln (22)

Apply log rule:

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

ln (22) = ln (2) + ln (2)

= ln (2) + ln (2)

ln (2) = \frac{1}{2} ln (2)

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

Factor out common term

ln (2)

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

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

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

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Frequently Asked Questions (FAQ)

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