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How do you find the inverse of #y=4^x#?

Answer 1

Madelyn Anderson

To find the inverse of a function, you swap the roles of x and y and then solve for the new y.

Given function: y = 4^x

Swap x and y: x = 4^y
Solve for y: Taking the logarithm of both sides (base 4 for convenience): log₄(x) = y

Therefore, the inverse of y = 4^x is y = log₄(x).

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Answer 2

Benjamin Achtenberg

#y=lnx/ln4#

Switch the places of #x, y# and subsequently solve for #y:#

#y=4^x#

#x=4^y#

#ln(4^y)=lnx#

We need to get an explicit solution, IE, isolate #y.# Recalling that #ln(a^b)=blna#:

#yln(4)=lnx#

#y=lnx/ln4#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.