which of the following is the inverse of y = 12^x?\no y = log_(1/12) x\no y = log_12 (1/x)\no y = log_x…
which of the following is the inverse of y = 12^x?\no y = log_(1/12) x\no y = log_12 (1/x)\no y = log_x 12\no y = log_12 x
Answer
Answer:
D. $y = \log_{12}x$
Explanation:
Step1: Recall the definition of inverse functions.
If $y = a^x$, then its inverse is $x=a^y$ rewritten in logarithmic - form. For the function $y = 12^x$, we swap $x$ and $y$ to get $x = 12^y$.
Step2: Convert the exponential equation to logarithmic form.
The exponential equation $x = 12^y$ in logarithmic form is $y=\log_{12}x$ according to the rule $a^b = c\Leftrightarrow\log_{a}c=b$.