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Popular >

simplify ln(5sqrt(5))

Solution

simplify

ln (55)

Solution

\frac{3}{2} ln (5)

+1

Decimal Notation

2.41415 \dots

Solution steps

ln (55)

Apply log rule:

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

ln (55) = ln (5) + ln (5)

= ln (5) + ln (5)

ln (5) = \frac{1}{2} ln (5)

= ln (5) + \frac{1}{2} ln (5)

Factor out common term

ln (5)

= ln (5) (1 + \frac{1}{2})

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

= \frac{3}{2} ln (5)

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Frequently Asked Questions (FAQ)

What is ln(5sqrt(5)) ?
The solution to ln(5sqrt(5)) is 3/2 ln(5)