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

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

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simplify 1/2 [ln(x+3)+ln(x)-ln(x^2-1)]

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (x + 3) + ln (x) = ln (x (x + 3))

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

Apply log rule:

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

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

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

Remove parentheses:

(a) = a

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

- lo g_{10} (4.18 \cdot 1 0^{- 4})

3 lo g_{10} (d) - lo g_{10} (k)

lo g_{4} (u^{3} v^{6})

lo g_{10} (\frac{2 x}{7})

3 lo g_{10} (x) + 6 lo g_{10} (x + 8)

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