What is 5/3 ln|5|-2/3 ln|2| ?

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

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simplify 5/3 ln|5|-2/3 ln|2|

simplify

\frac{5}{3} ln ∣ 5 ∣ - \frac{2}{3} ln ∣ 2 ∣

Decimal Notation

2.22029 \dots

Solution steps

\frac{5}{3} ln ∣ 5 ∣ - \frac{2}{3} ln ∣ 2 ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{5}{3} ln ∣ 5 ∣ = ln (∣ 5 ∣^{\frac{5}{3}})

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

= ln (\frac{∣ 5 ∣ ^{\frac{5}{3}}}{∣ 2 ∣ ^{\frac{2}{3}}})

lo g_{3} (\frac{1}{25 \cdot 3 \cdot 5})

- 0.14 lo g_{2} (0.14) + (- 0.86) lo g_{2} (0.86)

ln (4 x e^{- 20 x})

10 lo g_{10} (\frac{( 2.5 \cdot 1 0 ^{- 3} )}{1000}) + 40 + 59

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

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