What is ln((5\sqrt[3]{5})/2) ?

The solution to ln((5\sqrt[3]{5})/2) is 4/3 ln(5)-ln(2)

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simplify ln((5\sqrt[3]{5})/2)

simplify

\frac{4}{3} ln (5) - ln (2)

Decimal Notation

1.45277 \dots

Solution steps

Apply log rule:

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

= ln (5) + \frac{1}{3} ln (5) - ln (2)

Add similar elements:

ln (5) + \frac{1}{3} ln (5) = \frac{4}{3} ln (5)

= \frac{4}{3} ln (5) - ln (2)

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What is ln((5\sqrt[3]{5})/2) ?
The solution to ln((5\sqrt[3]{5})/2) is 4/3 ln(5)-ln(2)