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