To find the inverse of the function [tex]\( y = 12^x \)[/tex], follow these steps:
1. Replace [tex]\( y \)[/tex] with [tex]\( x \)[/tex] and [tex]\( x \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[
x = 12^y
\][/tex]
2. Solve for [tex]\( y \)[/tex]:
- To isolate [tex]\( y \)[/tex], take the logarithm base 12 of both sides:
[tex]\[
\log_{12}(x) = y
\][/tex]
3. Rewrite the equation:
- So, the inverse function is:
[tex]\[
y = \log_{12}(x)
\][/tex]
After following this process, we see that the correct inverse of the function [tex]\( y = 12^x \)[/tex] is:
[tex]\[
y = \log_{12} x
\][/tex]
Thus, among the given choices, the correct answer is:
\[
y = \log_{12} x
\
