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Which of the following is the inverse of [tex]$y=12^x$[/tex]?

A. [tex]$y=\log _{\frac{1}{12}} x$[/tex]
B. [tex][tex]$y=\log _{12} \frac{1}{x}$[/tex][/tex]
C. [tex]$y=\log _x 12$[/tex]
D. [tex]$y=\log _{12} x$[/tex]

Sagot :

GinnyAnswer
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
\
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