Question

How do I work out the problem 9^x-3^x-12=0 ? logarithmic function

Answer 1

gimmick is to write
\[9^x\] as
\[3^{2x}\] and solve a quadratic equation

Answer 2

i know the answer but trying to get teh answer is my problem

Answer 3

yea

Answer 4

im confused because you are using a different example :-(

Answer 5

original equation is
\[9^x-3^x-12=0\]

Answer 6

put
\[z=3^x\] get
\[z^2-z-12=0\]

Answer 7

factor as
\[(z-4)(z+3)=0\]
\[z=4, z=-3\]

Answer 8

so
\[3^x=4\] or
\[3^x=-3\] and the second one is not possible so only
\[3^x=4\]

Answer 9

that's wrong it can't be two different answers though?

Answer 10

now solve for x.
one solution is
\[x=\log_3(4)\]

Answer 11

no only one answer

Answer 12

the quadratic has two answers, but
\[3^x>0\] for all x so you can ignore
\[3^x=-3\]

Answer 13

i'm all ears

Answer 14

\[3^x=4\]

Answer 15

i used a calculator and got -12 as an answer

Answer 16

you want an actual number out of this right?

Answer 17

it says to solve the equation: 9 to the power of x minus 3 to the poewr of x minus 12 = 0

Answer 18

\[3^x=4\iff x = log_3(4)\iff x = \frac{\ln(4)}{\ln(3)}\]

Answer 19

got it, and you solution is above

Answer 20

if you want a decimal use a calculator,

Answer 21

i need to read it again. yes i can figure it out with a calculator :-) one sec

Answer 22

i will get rid of the junk

Answer 23

okay i prefer that :D

Answer 24

hmm?

Answer 25

how'd it go?

Answer 26

im just confused can you put exactly what u said in one line? :P so i can read it

Answer 27

to work it out, not the answer

Answer 28

yes

Answer 29

the trick is to recognize
\[9=3^2\] so
\[9^x=(3^2)^x=3^{2x}\]
then you have
\[3^{2x}-3^x-12=0\] which is a quadratic equation in
\[3^x\] because
\[3^{2x}=(3^x)^2\]
so to make life easy replace
\[z=3^x\] giving you the equation
\[z^2-z-12=0\]
\[(z-4)(z+3)=0\]
\[z=4,z=-3\]
now go back and replace
\[z\text{ by }3^x\] and get
\[3^x=4\] or
\[x^x=-3\] but there is no not about those damned way that
\[x^x=-3\] so only
\[3^x=4\] is a solution
now solve for x. you could say
\[x=\log_3(4)\] but that doesn't really give you a number for x. if you want a decimal use the change of base formula to get
\[x=\frac{\ln(4)}{\ln(3)}\] and then a calculator

Answer 30

wow i don't know where that line came from. what i meant is
THERE IS NO WAY THAT
\[3^x=-3\]

Answer 31

ok i understand, answer has to be positive.

Answer 32

But when I input 4 for x , 9^4-3^4-12 doesn't equal zero?

Answer 33

woops ignore that last msg

Answer 34

whew

Answer 35

http://www.wolframalpha.com/input/?i=ln%284%29%2Fln%283%29

Answer 36

you are right I get it now. Answer is correct.

Answer 37

hurrah!

Answer 38

this is my first time here, how do i give you a medal?

Answer 39

http://www.wolframalpha.com/input/?i=ln%284%29%2Fln%283%29

Answer 40

i figured that out :P thanks so much.