Posted by **Kenya** on Sunday, May 1, 2011 at 11:45am.

How do you find the inverse of functions? for example how would you find the inverse of y= log8 x

- Algebra -
**MathMate**, Sunday, May 1, 2011 at 12:00pm
Let's try this for f(x)= y = e^(6x)

Step 1:

interchange x and y to get

x=e^(6y)

Step 2:

solve for y in terms of x:

ln(x) = ln(e^(6y)) = 6y

y = ln(x)/6

So

f^{-1}(x) = ln(x)/6

Step 3:

Verify that f(f^{-1}(x))=x (if the inverse was correct).

f(f^{-1}(x))

=f(ln(x)/6)

=e^(6*ln(x)/6)

=e^(ln(x))

=x

So the inverse is correct.

- Algebra -
**Kenya**, Sunday, May 1, 2011 at 12:23pm
Ok that's slightly confusing.

I understand the flipping of x and y but then what do you do?

so x=log8 y

?

- Algebra -
**MathMate**, Sunday, May 1, 2011 at 1:34pm
Yes, then you solve for y in terms of x.

use the law of exponents:

e^{log(x)}=x

or

8^{log8 y}=y, etc.

(assuming log8 y is log(y) to the base 8)

raise both sides to power of 8 to get

8^{x} = 8^{log8(y)<?sup>
Simplify and solve y in terms of x.
}

- Algebra - typo -
**MathMate**, Sunday, May 1, 2011 at 1:43pm
8^{x} = 8^{log8(y)} = y

Simplify and solve y in terms of x.

- Algebra -
**Webber**, Sunday, May 1, 2011 at 1:49pm
MMMMmmmmmmk that helps, thanks!

- Algebra :) -
**MathMate**, Sunday, May 1, 2011 at 2:54pm
You're welcome!

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