Solve for x over the real numbers:
log(5, 2) - log(5, x + 7) = 1
log(5, 2) - log(5, x + 7) = log(2)/log(5) - log(x + 7)/log(5):
log(2)/log(5) - log(x + 7)/log(5) = 1
Rewrite the left hand side by combining fractions. log(2)/log(5) - log(x + 7)/log(5) = (log(2) - log(x + 7))/log(5):
(log(2) - log(x + 7))/log(5) = 1
Multiply both sides by log(5):
log(2) - log(x + 7) = log(5)
Subtract log(2) from both sides:
-log(x + 7) = log(5) - log(2)
Multiply both sides by -1:
log(x + 7) = log(2) - log(5)
log(2) - log(5) = log(2) + log(1/5) = log(2) + log(1/5) = log(2/5) = log(2/5):
log(x + 7) = log(2/5)
Cancel logarithms by taking exp of both sides:
x + 7 = 2/5
Subtract 7 from both sides:
Answer: x = -33/5