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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Combine same powers :

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

8 ln (x + 8) - 8 ln (x)

ln (\frac{273}{293}) \cdot 1.3

ln (1.7 \cdot 1 0^{9})

\frac{1}{2} ln (10) + \frac{1}{2} ln (20)

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

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