1. exponential inverse problem

need the answer to this question asap.

2. Re: exponential inverse problem

Hello, rainxspear!

Do you know the procedure for finding an inverse function?

If $f(x) \:=\:\log_4(x+5)+3,$
what is the function $g(x)$ if $f(x)$ and $g(x)$ are inverses?

$\text{We have: }\:y \;=\;\log_4(x+5)+3$

$\text{Interchange }x\text{ and }y\!: \;x \:=\:\log_4(y+5) + 3$

$\text{Solve for }y\!:\;x - 3 \;=\;\log_4(y+5)$

= . . . . . . . . $4^{x-3} \;=\;y+5$

. . . . . . . $4^{x-3} - 5 \;=\;y$

Therefore: . $g(x) \;=\;4^{x-3} - 5$

3. Re: exponential inverse problem

Thank you so much, that cleared up things so immensely.

4. Re: exponential inverse problem

One way to solve these inverse problems is: (1) state f(x) = y, (2) solve for x in terms of y, (3) switch x and y, and (4) replace y with g(x), you are done.

So y = what?

So x = what?

What do you get when you switch x and y?

I'll get you started.

$f(x) = log_4(x + 5) - 3.$

$y = log_4(x + 5) - 3 \implies y + 3 = log_4(x + 5) \implies x + 5 = 4^{y - 3} \implies what?$