Answer
$\displaystyle \log\frac{x(x-1)}{7}$
Work Step by Step
$\log x+\log(x^{2}-1)-\log 7-\log(x+1)=$
... group all positive signed terms; group all negative signed terms
$=[\log x+\log(x^{2}-1)]-[\log 7+\log(x+1)]$
... apply the product rule to each bracket
$=\log[x(x^{2}-1)]-\log[7(x+1)]$
... apply the quotient rule
$=\displaystyle \log\frac{x(x^{2}-1)}{7(x+1)}$
... recognize a difference of squares in the numerator
$=\displaystyle \log\frac{x(x+1)(x-1)}{7(x+1)}$
... cancel the common term
$=\displaystyle \log\frac{x(x-1)}{7}$
