Question

write the expression below as a single logarithm show work.

ln(x-7/x^2+12x+36)-ln(x^2-49/x+6)

Answer 1

first

x^2+12x+36 = (x+6)(x+6)
so

ln of

(x-7)(x+6)
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(x+6)(x+6)(x+7)(x-7)

ln of

1
=====================
(x+6)(x+1)

= ln 1 - ln(x^2 +7x + 6)
but ln 1 = 0
so
- ln (x^2 + 7 x + 6)