Question

solve for x
http://media.apexlearning.com/Images/200709/24/2b04270b-90ae-4585-b318-f39528609bda.gif

Answer 1

okay lets see
log9X=3/2
the nine is little and lower down

Answer 2

\[\log _{9}x = \frac{ 3 }{ 2 }\]

Like that @aly_peters?

Answer 3

https://en.wikibooks.org/wiki/LaTeX
\[\Large\begin{array}{rl}log_9x&=&\frac32\\9^{log_9x}&=&9^\frac32\\x&=&9^\frac32=9^{1.5}\end{array}\]

Answer 4

yes @RICARDOismyfirstname

Answer 5

http://www.wolframalpha.com/input/?i=solve+log_9%28x%29%3D%283%29%2F%282%29

look under the "Result:" tab

Answer 6

Thanks! but does anyone know how to actually solve?

Answer 7

kc did a nice solution process

Answer 8

ohh, just kinda hard to read lol

Answer 9

but i see now

Answer 10

:)

Answer 11

That's how to solve it @aly_peters

Answer 12

when you see log base 9 think exponents to "undo the log"
kc showed how to use base 9 to the log power to undo the log.
in other words

\[ 9^{\log_9(x) } = x \]
if you have an equation you have to do the same thing to both sides
\[ \log_9(x)= \frac{3}{2} \\
9^{\log_9(x) } = 9^{\frac{3}{2} } \\
x = 9^{\frac{3}{2} }\]

now it is good to know that \[x^{\frac{1}{2}} = \sqrt{x} \]
also, you should know
\[ x^{\frac{3}{2}}= \left(x^{\frac{1}{2}}\right)^3 \]
in other words, for your problem
\[ x = 9^{\frac{3}{2} } \\
x= \left(9^{\frac{1}{2}}\right)^3 \\
x= \left(\sqrt{9}\right)^3
\]

Answer 13

thanks everyone, its a big help(:

Answer 14

thanks @phi (: