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Popular >

simplify ln(8/(3*sqrt(3)))

Solution

simplify

ln (\frac{8}{3 \cdot 3})

Solution

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

+1

Decimal Notation

0.43152 \dots

Solution steps

ln (\frac{8}{3 3})

Apply log rule:

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

ln (\frac{8}{3 3}) = ln (8) - ln (33)

= ln (8) - ln (33)

Apply log rule:

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

ln (33) = ln (3) + ln (3)

= ln (8) - (ln (3) + ln (3))

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

= ln (8) - \frac{3}{2} ln (3)

ln (8) = 3 ln (2)

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

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Frequently Asked Questions (FAQ)

What is ln(8/(3*sqrt(3))) ?
The solution to ln(8/(3*sqrt(3))) is 3ln(2)-3/2 ln(3)