What is ln((3^{3/8})/3) ?

The solution to ln((3^{3/8})/3) is -5/8 ln(3)

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simplify ln((3^{3/8})/3)

simplify

ln (\frac{3 ^{\frac{3}{8}}}{3})

- \frac{5}{8} ln (3)

Decimal Notation

- 0.68663 \dots

Solution steps

ln (\frac{3 ^{\frac{3}{8}}}{3})

Apply log rule:

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

ln (\frac{3 ^{\frac{3}{8}}}{3}) = ln (3^{\frac{3}{8}}) - ln (3)

= ln (3^{\frac{3}{8}}) - ln (3)

Apply log rule:

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

ln (3^{\frac{3}{8}}) = \frac{3}{8} ln (3)

= \frac{3}{8} ln (3) - ln (3)

Factor out common term

ln (3)

= ln (3) (\frac{3}{8} - 1)

\frac{3}{8} - 1 = - \frac{5}{8}

= - \frac{5}{8} ln (3)

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