Solve log_b(x) = c for x in terms of b and c.

• A. x = c^b
• B. x = log_b(c)
• C. x = b^c
• D. x = b + c

Answer: (C)

The key idea is the inverse relationship between logarithms and exponents. If log base b of x equals c, then x is exactly the number you get by raising b to the power c. In symbols, b^c = x. To see this, raise b to the power of both sides: b^{log_b(x)} = b^c. The left side simplifies to x, so x = b^c. This also fits the domain: the log is defined when b > 0 and b ≠ 1, and x > 0, with c any real number. The expression b^c is the correct form because it directly encodes the inverse relationship.