What is (1/2)^3-24ln(1/2)+8 ?

The solution to (1/2)^3-24ln(1/2)+8 is 24ln(2)+65/8

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simplify (1/2)^3-24ln(1/2)+8

simplify

(\frac{1}{2})^{3} - 24 ln (\frac{1}{2}) + 8

24 ln (2) + \frac{65}{8}

Decimal Notation

24.76053 \dots

Solution steps

(\frac{1}{2})^{3} - 24 ln (\frac{1}{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)

= (\frac{1}{2})^{3} - 24 (ln (1) - ln (2)) + 8

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

24 (ln (1) - ln (2)) = - 24 ln (2)

= \frac{1}{2 ^{3}} - (- 24 ln (2)) + 8

Apply rule

- (- a) = a

= \frac{1}{2 ^{3}} + 24 ln (2) + 8

2^{3} = 8

= \frac{1}{8} + 24 ln (2) + 8

Combine the fractions

8 + \frac{1}{8} : \frac{65}{8}

= 24 ln (2) + \frac{65}{8}

(\frac{1}{2})^{3} - 24 ln (\frac{1}{2}) + 3

ln (\frac{5000}{200})

2 lo g_{10} (7) + 3 lo g_{10} (x)

\frac{1}{7} [ln (x) - ln (x + 4)]

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

What is (1/2)^3-24ln(1/2)+8 ?
The solution to (1/2)^3-24ln(1/2)+8 is 24ln(2)+65/8