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Popular >

simplify ln(4sqrt(2))

Solution

simplify

ln (42)

Solution

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

+1

Decimal Notation

1.73286 \dots

Solution steps

ln (42)

Apply log rule:

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

ln (42) = ln (4) + ln (2)

= ln (4) + ln (2)

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

= ln (4) + \frac{1}{2} ln (2)

ln (4) = 2 ln (2)

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

Factor out common term

ln (2)

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

2 + \frac{1}{2} = \frac{5}{2}

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

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Frequently Asked Questions (FAQ)

What is ln(4sqrt(2)) ?
The solution to ln(4sqrt(2)) is 5/2 ln(2)