What is ln((2/3 x+1)/(2/3 x-1)) ?

The solution to ln((2/3 x+1)/(2/3 x-1)) is ln((2x)/3+1)-ln((2x)/3-1)

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simplify ln((2/3 x+1)/(2/3 x-1))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Multiply

\frac{2}{3} x : \frac{2 x}{3}

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

Multiply

\frac{2}{3} x : \frac{2 x}{3}

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

ln (10000) - ln (5000) + 5

ln (\frac{24}{5})

+ \frac{ln ( 1.5575 )}{ln ( \frac{2}{25} ) - ln ( 0.239 )}

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

ln (\frac{25}{14}) + 10

What is ln((2/3 x+1)/(2/3 x-1)) ?
The solution to ln((2/3 x+1)/(2/3 x-1)) is ln((2x)/3+1)-ln((2x)/3-1)