What is expand 2[ln(x)-ln(x+5)-ln(x-5)] ?

The solution to expand 2[ln(x)-ln(x+5)-ln(x-5)] is 2ln(x/(x^2-25))

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expand 2[ln(x)-ln(x+5)-ln(x-5)]

expand

2 [ln (x) - ln (x + 5) - ln (x - 5)]

2 ln (\frac{x}{x ^{2} - 25})

Solution steps

2 [ln (x) - ln (x + 5) - ln (x - 5)]

Apply log rule:

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

ln (x) - ln (x + 5) = ln (\frac{x}{x + 5})

= 2 [ln (\frac{x}{x + 5}) - ln (x - 5)]

Apply log rule:

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

ln (\frac{x}{x + 5}) - ln (x - 5) = ln (\frac{\frac{x}{x + 5}}{x - 5})

= 2 [ln (\frac{\frac{x}{x + 5}}{x - 5})]

Expand

\frac{\frac{x}{x + 5}}{x - 5} : \frac{x}{x ^{2} - 25}

= 2 [ln (\frac{x}{x ^{2} - 25})]

Remove parentheses:

(a) = a

= 2 ln (\frac{x}{x ^{2} - 25})

ln (\frac{4}{e ^{3 x - 1}})

ln (2.8 \cdot \frac{( 5 - 1.8 )}{1.8 \cdot ( 5 - 2.8 )})

4 ln ∣ x - 2 ∣ + 10 ln ∣ x + 5 ∣

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

ln (y) + ln (cos (v))

What is expand 2[ln(x)-ln(x+5)-ln(x-5)] ?
The solution to expand 2[ln(x)-ln(x+5)-ln(x-5)] is 2ln(x/(x^2-25))