What is ln(1/2 (2+sqrt(8))) ?

The solution to ln(1/2 (2+sqrt(8))) is ln(2+2sqrt(2))-ln(2)

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simplify ln(1/2 (2+sqrt(8)))

simplify

ln (\frac{1}{2} (2 + 8))

ln (2 + 22) - ln (2)

Decimal Notation

0.88137 \dots

Solution steps

ln (\frac{1}{2} (2 + 8))

Apply log rule:

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

ln (\frac{1}{2} (2 + 8)) = ln (\frac{1}{2}) + ln (2 + 8)

= ln (\frac{1}{2}) + ln (2 + 8)

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

= ln (1) - ln (2) + ln (2 + 8)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (2) + ln (2 + 8)

8 = 22

= 0 - ln (2) + ln (2 + 22)

0 - ln (2) + ln (2 + 22) = - ln (2) + ln (2 + 22)

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

lo g_{10} (z^{5} y)

lo g_{10} (x^{7} y)

- ln (3.02 \cdot 1 0^{- 8})

ln (3) - ln (10)

What is ln(1/2 (2+sqrt(8))) ?
The solution to ln(1/2 (2+sqrt(8))) is ln(2+2sqrt(2))-ln(2)