What is 3[ln(x)-ln(x+9)-ln(x-9)] ?

The solution to 3[ln(x)-ln(x+9)-ln(x-9)] is 3ln(x/((x+9)(x-9)))

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simplify 3[ln(x)-ln(x+9)-ln(x-9)]

simplify

3 [ln (x) - ln (x + 9) - ln (x - 9)]

3 ln (\frac{x}{( x + 9 ) ( x - 9 )})

Solution steps

3 [ln (x) - ln (x + 9) - ln (x - 9)]

Apply log rule:

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

ln (x) - ln (x + 9) = ln (\frac{x}{x + 9})

= 3 [ln (\frac{x}{x + 9}) - ln (x - 9)]

Apply log rule:

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

ln (\frac{x}{x + 9}) - ln (x - 9) = ln (\frac{\frac{x}{x + 9}}{x - 9})

= 3 [ln (\frac{\frac{x}{x + 9}}{x - 9})]

Apply the fraction rule:

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

= 3 [ln (\frac{x}{( x + 9 ) ( x - 9 )})]

Remove parentheses:

(a) = a

= 3 ln (\frac{x}{( x + 9 ) ( x - 9 )})

ln (\frac{x}{20})

- 3 ln (x) + \frac{5}{2} ln (x^{2} + x + 6)

lo g_{3} (\frac{1}{x ^{2} y 3 ^{z}})

ln (\frac{273}{259})

4 lo g_{b} (y) + 3 lo g_{b} (x)

What is 3[ln(x)-ln(x+9)-ln(x-9)] ?
The solution to 3[ln(x)-ln(x+9)-ln(x-9)] is 3ln(x/((x+9)(x-9)))