If log_b(a) = c, which equation is equivalent?

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Multiple Choice

If log_b(a) = c, which equation is equivalent?

Explanation:
The key idea is the inverse relationship between logarithms and exponents. If log base b of a equals c, that means the exponent you must raise b to in order to get a is c. So b raised to the power c equals a. In symbols, b^c = a. This is exactly the direct restatement of the given information. The other forms would imply different relationships (for example, a = c^b would mean a is c raised to b, not b raised to c; a = log_b(c) would require c = b^a). Therefore, the equivalent equation is b^c = a.

The key idea is the inverse relationship between logarithms and exponents. If log base b of a equals c, that means the exponent you must raise b to in order to get a is c. So b raised to the power c equals a. In symbols, b^c = a. This is exactly the direct restatement of the given information. The other forms would imply different relationships (for example, a = c^b would mean a is c raised to b, not b raised to c; a = log_b(c) would require c = b^a). Therefore, the equivalent equation is b^c = a.

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