What does b^log(x) equal to?

To understand why the expression ( b^{\log(x)} ) is equal to ( x ), we can apply fundamental properties of logarithms and exponents.

The term ( \log(x) ) represents the logarithm of ( x ) to the base ( b ). This means that if you raise ( b ) to the power of ( \log(x) ), you are essentially undoing the logarithm.

According to the definition of logarithms, if ( y = \log_b(x) ), then it follows that ( b^y = x ). In this case, if we let ( y = \log(x) ), then by the aforementioned property of logarithms, ( b^{\log(x)} ) translates directly to ( x ).

Thus, when you compute ( b^{\log(x)} ), you are finding that raising ( b ) to the power of the logarithm (which is the power to which ( b ) must be raised to obtain ( x )) yields ( x ) itself, confirming that the correct answer is ( x ).