How do you find the inverse of y=log_x4?

1 Answer
Mar 28, 2018

y=4^{1/x}

Explanation:

I would recommend using the base change rule for this one.

log_ba=log_ca/log_cb

Let's express log_x4 as ln4/lnx

(Note: As an IB student I use ln to denote log base e (log_ex). I am aware that there may be different conventions regarding this depending on region/educational system etc.)

Therefore y = ln4/lnx

We rearrange the equation to isolate x.

ln4/y = lnx

Rewrite the equation using e raised to the power of both sides so that the equation is equal to x.

e^{ln4/y} = e^{lnx}=x

Using the relation a^{x} = e^{xlna} we can write e^{ln4/y} as 4^{1/y}.

This gives us x=4^{1/y}

Having rearranged the equation all we need to do is swap y and x to find the inverse.

y=4^{1/x}