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Popular >

simplify (1/2)^{-3}ln(2(1/2))

Solution

simplify

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

Solution

0

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Multiply:

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

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

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

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

Multiply

2 \cdot \frac{1}{2} : 1

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

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

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

Apply rule

\frac{a}{1} = a

= 2^{3} ln (1)

Simplify

ln (1) : 0

= 2^{3} \cdot 0

Apply rule

0 \cdot a = 0

= 0

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Frequently Asked Questions (FAQ)

What is (1/2)^{-3}ln(2(1/2)) ?
The solution to (1/2)^{-3}ln(2(1/2)) is 0