What is ln((2^{3/4})/2) ?

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

Popular >

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

simplify

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

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

Decimal Notation

- 0.17328 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Factor out common term

ln (2)

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

\frac{3}{4} - 1 = - \frac{1}{4}

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

- ln (4 e^{- 8})

ln (\frac{1}{x + h} + 1) - ln (\frac{1}{x} + 1)

ln (1 + \frac{y ^{2}}{x ^{2}}) + ln (x)

- 1.44 - 5 lo g_{10} (\frac{2.6}{10})

ln (4 x) + ln (x^{2})