What is the inverse of the function $y=log_4 x$ ?

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Answer 1 · 2016-09-06T17:06:49

$f^(- 1)(x) = 4^(x)$

We have: $y = log_(4)(x)$

Let's begin by interchanging the variables:

$=> x = log_(4)(y)$

In order to determine the inverse of the function, we must solve for $y$ .

Using the laws of logarithms:

$=> y = 4^(x)$

Finally, let's replace $y$ with $f^(- 1)(x)$ :

$=> f^(- 1)(x) = 4^(x)$

Answer 2 · 2016-09-07T15:19:49

$y=4^x$

Given: $" "y=log_4(x)$

Another way of writing this is

$4^y=x$

Where there is a $y$ write $x$
Where there is a $x$ write $y$

$4^x=y" "larr" Function inverse"$

The function inverse is a reflection of the original equation about the straight line $y=x$

Tony B

What is the inverse of the function y=log_4 xy=log_4 x?