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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

2 ln (x) = ln (x^{2})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

- 0.7 \cdot lo g_{2} (0.7) - 0.3 lo g_{2} (0.3)

ln (\frac{2.3}{1.5})

2 (ln (2 + 1) - ln (2 - 1))

lo g_{30} (15 0^{\circ})

ln (\frac{0.0136446}{0.00350107})

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