Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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
\
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.