Answer
Option (b)
Work Step by Step
RECALL:
$e^{b\cdot \ln{a}}=a^b$
(a) $e^{2x} \ne 2^x$
(b) Using the property in the recall part above gives:
$e^{x\cdot\ln{2}} = 2^x$
(c) $e^{\log_2{x}} \ne 2^x$
(d) Using the property in the recall part above gives:
$e^{2\cdot\ln{x}} = x^2$
Thus, only the expression in Option (b) is equivalent to $2^x$.
