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

The solution to ln(1/(2sqrt(2))) is -3/2 ln(2)

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

simplify

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

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

Decimal Notation

- 1.03972 \dots

Solution steps

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

Apply log rule:

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

ln (\frac{1}{2 2}) = ln (1) - ln (22)

= ln (1) - ln (22)

Apply log rule:

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

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

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

ln (1) = 0

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

= 0 - \frac{3}{2} ln (2)

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

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

10.33 - (- 15.98) + 10 lo g_{10} (\frac{800}{600})

lo g_{10} (a) + 7 lo g_{10} (b)

3 lo g_{3} (x + 3) (lo g_{3} (w) - 4 lo g_{3} (y))

ln (a) - ln (c)

ln ((x - 1)^{\frac{1}{2}}) + ln ((x + 1)^{\frac{- 3}{2}})