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Popular >

simplify ln(1/(2^{3/4)})

Solution

simplify

ln (\frac{1}{2 ^{\frac{3}{4}}})

Solution

- \frac{3}{4} ln (2)

+1

Decimal Notation

- 0.51986 \dots

Solution steps

ln (\frac{1}{2 ^{\frac{3}{4}}})

Apply log rule:

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

ln (\frac{1}{2 ^{\frac{3}{4}}}) = ln (1) - ln (2^{\frac{3}{4}})

= ln (1) - ln (2^{\frac{3}{4}})

Apply log rule:

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

ln (2^{\frac{3}{4}}) = \frac{3}{4} ln (2)

= ln (1) - \frac{3}{4} ln (2)

Apply log rule:

lo g_{a} (1) = 0

= 0 - \frac{3}{4} ln (2)

0 - \frac{3}{4} ln (2) = - \frac{3}{4} ln (2)

= - \frac{3}{4} ln (2)

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Frequently Asked Questions (FAQ)

What is ln(1/(2^{3/4)}) ?
The solution to ln(1/(2^{3/4)}) is -3/4 ln(2)