What is (3/2 ln|b^3+1|-ln|3b+1|)/3 ?

The solution to (3/2 ln|b^3+1|-ln|3b+1|)/3 is (ln((|b^3+1|^{3/2})/(|3b+1|)))/3

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simplify (3/2 ln|b^3+1|-ln|3b+1|)/3

simplify

\frac{\frac{3}{2} ln b ^{3} + 1 - ln ∣ 3 b + 1 ∣}{3}

\frac{ln ( \frac{∣ b ^{3} + 1 ∣ ^{\frac{3}{2}}}{∣ 3 b + 1 ∣} )}{3}

Solution steps

\frac{\frac{3}{2} ln b ^{3} + 1 - ln ∣ 3 b + 1 ∣}{3}

Apply log rule:

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

\frac{3}{2} ln b^{3} + 1 = ln (b^{3} + 1^{\frac{3}{2}})

= \frac{ln ( b ^{3} + 1 ^{\frac{3}{2}} ) - ln ∣ 3 b + 1 ∣}{3}

Apply log rule:

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

ln (b^{3} + 1^{\frac{3}{2}}) - ln ∣ 3 b + 1 ∣ = ln \frac{b ^{3} + 1 ^{\frac{3}{2}}}{∣ 3 b + 1 ∣}

= \frac{ln ( \frac{∣ b ^{3} + 1 ∣ ^{\frac{3}{2}}}{∣ 3 b + 1 ∣} )}{3}

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

ln (\frac{273}{264})

ln (\frac{a + a ^{2} + x ^{2}}{x})

- ln (3) - ln (x) - ln (5 x)

- lo g_{2} (\frac{1}{10})

What is (3/2 ln|b^3+1|-ln|3b+1|)/3 ?
The solution to (3/2 ln|b^3+1|-ln|3b+1|)/3 is (ln((|b^3+1|^{3/2})/(|3b+1|)))/3