Which expression is equivalent to b^logb(A)?

The expression ( b^{\log_b(A)} ) is based on the properties of logarithms and exponents. Specifically, it utilizes the fundamental relationship between logarithms and exponentials: ( b^{\log_b(x)} = x ) for any positive value ( x ).

In this case, by substituting ( A ) for ( x ), we directly apply the property: ( b^{\log_b(A)} = A ). This means that raising ( b ) to the power of the logarithm of ( A ) (to the base ( b )) results in ( A ) itself.

Therefore, the correct expression equivalent to ( b^{\log_b(A)} ) is indeed ( A ). This illustrates a key principle in mathematics about how logarithmic and exponential functions are inverses of each other, allowing one to 'undo' the operation of the other.