Question

question 23/24
23 find the inverse of $y = 2^x$.
a $x = 2^y$
b $y = 2x$
c $y = \log_2 x$
d $y = 2\log x$

Explanation:

Step1: Swap x and y

Given \( y = 2^x \), swap \( x \) and \( y \) to get \( x = 2^y \).

Step2: Solve for y

To solve \( x = 2^y \) for \( y \), we use the logarithmic form. Recall that if \( a^b = c \), then \( \log_a c = b \). Here, \( a = 2 \), \( b = y \), and \( c = x \), so \( y=\log_2 x \).

Answer:

C. \( y = \log_{2} x \)