What is 1/3 (ln(x/3+1)-ln(x/3-1)) ?

The solution to 1/3 (ln(x/3+1)-ln(x/3-1)) is 1/3 ln((x+3)/(x-3))

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simplify 1/3 (ln(x/3+1)-ln(x/3-1))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

\frac{\frac{x}{3} + 1}{\frac{x}{3} - 1} : \frac{x + 3}{x - 3}

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

- (\frac{3}{14}) lo g_{2} (\frac{3}{14}) - (\frac{2}{14}) lo g_{2} (\frac{2}{14})

ln (\frac{28500}{19250})

3 lo g_{2} (5) - lo g_{2} (3) + lo g_{2} (6)

\frac{1}{3} (6 ln (x + 4) + ln (x) - ln (x^{2} - 8))

\frac{ln ( \frac{3}{2} )}{8 ln ( 10 )}

What is 1/3 (ln(x/3+1)-ln(x/3-1)) ?
The solution to 1/3 (ln(x/3+1)-ln(x/3-1)) is 1/3 ln((x+3)/(x-3))