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Popular >

simplify ln(1/(2^3))

Solution

simplify

ln (\frac{1}{2 ^{3}})

Solution

- 3 ln (2)

+1

Decimal Notation

- 2.07944 \dots

Solution steps

ln (\frac{1}{2 ^{3}})

Apply log rule:

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

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

= ln (1) - ln (2^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (2^{3}) = 3 ln (2)

= ln (1) - 3 ln (2)

Apply log rule:

lo g_{a} (1) = 0

= 0 - 3 ln (2)

0 - 3 ln (2) = - 3 ln (2)

= - 3 ln (2)

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Frequently Asked Questions (FAQ)

What is ln(1/(2^3)) ?
The solution to ln(1/(2^3)) is -3ln(2)