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

The solution to ln((5sqrt(2))/(\sqrt[3]{3)}) is ln(5)+1/2 ln(2)-1/3 ln(3)

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

simplify

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

Decimal Notation

1.58980 \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 (52) = ln (5) + ln (2)

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

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

f (x) = lo g_{2} (x - 4) + 3 lo g_{2} (x)

- lo g_{10} (1.41 x 1 0^{- 11})

4 lo g_{2} (x) + lo g_{2} (3)

ln (- 3 e^{- 4 t})

ln (e^{2 x} \cdot x \cdot x^{4} + 2 x^{2} + 1)

What is ln((5sqrt(2))/(\sqrt[3]{3)}) ?
The solution to ln((5sqrt(2))/(\sqrt[3]{3)}) is ln(5)+1/2 ln(2)-1/3 ln(3)