What is 6[ln(x)-ln(x+7)-ln(x-7)] ?

The solution to 6[ln(x)-ln(x+7)-ln(x-7)] is 6ln(x/((x+7)(x-7)))

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simplify 6[ln(x)-ln(x+7)-ln(x-7)]

simplify

6 [ln (x) - ln (x + 7) - ln (x - 7)]

6 ln (\frac{x}{( x + 7 ) ( x - 7 )})

Solution steps

6 [ln (x) - ln (x + 7) - ln (x - 7)]

Apply log rule:

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

ln (x) - ln (x + 7) = ln (\frac{x}{x + 7})

= 6 [ln (\frac{x}{x + 7}) - ln (x - 7)]

Apply log rule:

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

ln (\frac{x}{x + 7}) - ln (x - 7) = ln (\frac{\frac{x}{x + 7}}{x - 7})

= 6 [ln (\frac{\frac{x}{x + 7}}{x - 7})]

Apply the fraction rule:

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

= 6 [ln (\frac{x}{( x + 7 ) ( x - 7 )})]

Remove parentheses:

(a) = a

= 6 ln (\frac{x}{( x + 7 ) ( x - 7 )})

lo g_{π} (2 π)

ln (a \cdot T^{n})

lo g_{3} (\frac{1}{18})

ln (\frac{16}{28})

lo g_{1.5} (\frac{x}{4}) + 1

What is 6[ln(x)-ln(x+7)-ln(x-7)] ?
The solution to 6[ln(x)-ln(x+7)-ln(x-7)] is 6ln(x/((x+7)(x-7)))