# Expontial functions

• March 31st 2013, 01:20 PM
Melcarthus
Expontial functions
How does 9^x=3 nine to the x = 3

(1/9)-x 3^2=9
(1/3)^-2=9

• March 31st 2013, 01:24 PM
Plato
Re: Expontial functions
Quote:

Originally Posted by Melcarthus
How does 9^x=3

$\sqrt{9}=(9)^{\tfrac{1}{2}}=3$
• March 31st 2013, 05:08 PM
Soroban
Re: Expontial functions
He4llo, Melcarthus!

I have no idea what your steps mean.

Quote:

$\text{How does }\,9^x\,=\,3$
$(1/9)-x \qquad\qquad 3^2\,=\,9$ . ?
. . . . . . . . . . . . $\left(\tfrac{1}{3}\right)^{-2}\:=\:9$ . ?

$\text{Answer should be: }\:9^{\frac{1}{2}}$ . . . . no

We have: . $9^x \;=\;3$

. . . . . . $(3^2)^x \;=\;3$

. . . . . . . $3^{2x} \;=\;3^1$

Hence: . . $2x \;=\;1$

. . . . . . . . $x \;=\;\tfrac{1}{2}$