Solve for n:
log(7) + log(n - 2) = log(6 n)
Subtract log(6 n) from both sides:
log(7) + log(n - 2) - log(6 n) = 0
log(7) + log(n - 2) - log(6 n) = log(7) + log(n - 2) + log(1/(6 n)) = log((7 (n - 2))/(6 n)):
log((7 (n - 2))/(6 n)) = 0
Cancel logarithms by taking exp of both sides:
(7 (n - 2))/(6 n) = 1
Multiply both sides by 6 n:
7 (n - 2) = 6 n
Expand out terms of the left hand side:
7 n - 14 = 6 n
Subtract 6 n - 14 from both sides:
Answer: |n = 14