Question - Inverse of Exponential Function
Solution:
The question asks for the inverse of the exponential function $$ y = 4^x $$.To find the inverse function, we typically swap $$ x $$ and $$ y $$ and then solve for $$ y $$.Starting with $$ y = 4^x $$, we swap $$ x $$ and $$ y $$ to get $$ x = 4^y $$.Now we need to solve for $$ y $$. To do this, we take the logarithm base 4 of both sides:$$ \log_4(x) = \log_4(4^y) $$.Using the property of logarithms that $$ \log_b(b^a) = a $$, we simplify the right side to get:$$ \log_4(x) = y $$.So, the inverse function of $$ y = 4^x $$ is $$ y = \log_4(x) $$.The correct answer is:C. $$ y = \log_4(x) $$.
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