What is 4[ln(x)-ln(x+7)-ln(x-7)] ?

The solution to 4[ln(x)-ln(x+7)-ln(x-7)] is 4ln(x/((x+7)(x-7)))

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simplify 4[ln(x)-ln(x+7)-ln(x-7)]

simplify

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

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

Solution steps

4 [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})

= 4 [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})

= 4 [ln (\frac{\frac{x}{x + 7}}{x - 7})]

Apply the fraction rule:

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

= 4 [ln (\frac{x}{( x + 7 ) ( x - 7 )})]

Remove parentheses:

(a) = a

= 4 ln (\frac{x}{( x + 7 ) ( x - 7 )})

ln (\frac{x c}{m})

4 ln (9 x) + 4

7 ln (7) (ln (6) - ln (2))

4 ln (6) - 4 ln (3)

- lo g_{10} (5.6 \cdot 1 0^{- 7})

What is 4[ln(x)-ln(x+7)-ln(x-7)] ?
The solution to 4[ln(x)-ln(x+7)-ln(x-7)] is 4ln(x/((x+7)(x-7)))