What is 1/2 (ln(3)-ln|2e^{3x}+1|) ?

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

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simplify 1/2 (ln(3)-ln|2e^{3x}+1|)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{6} (x y^{3} z^{- 2})

lo g_{3} (\frac{27}{x + 7})

ln (l + x^{2} + y^{2}) - ln (x)

- 4 (ln ∣ 2 a - 10 ∣ - ln (10))

lo g_{3} (\frac{81}{x - 9})

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