Question

3^{2x}-3^{x+1}+8/9=0

Answer 1

\[3^{x}=t\]

Answer 2

\[3^{2x}-3^{x}.3^{1}+8/9=0\]

Answer 3

\[t ^{2}-3t+8/9=0\]

Answer 4

hope you can solve now.....

Answer 5

use nitz method!1

Answer 6

0.45
-3.45
i got it.

Answer 7

is it rite??
@nitz

Answer 8

that is t now subs t = 3^x

Answer 9

i am getting t=1/3 and t=8/3.

Answer 10

how can i slove 8/9

-3+-\[-3+-\sqrt{3^{2}}+4*1*8/9/2*1\]

Answer 11

what is it?????

Answer 12

\[-3+-\sqrt{9+32/9}/2\]

Answer 13

\[9t ^{2}-27t+8=0\]

Answer 14

okk

Answer 15

this is the required quadratic i am getting........
it can be factorised into linear factors

Answer 16

k

Answer 17

I GOT
1/3 and 8/3

Answer 18

the quadratic formula is
\[ t= \frac{1}{2}(-b ± \sqrt{b^2-4ac} ) \]
for your problem
\[ t^2- 3 t +\frac{8}{9} =0 \]
you get
\[ t= \frac{1}{2}(-(-3) ± \sqrt{9-\frac{32}{9}}) \]

Answer 19

@nitz thanks

Answer 20

i m confused

which answer is right
@nitz and @phi

Answer 21

that simplfies to
\[ t= \frac{1}{2}(3±\sqrt{\frac{49}{9}} ) \]
or
\[ t= \frac{3}{2} ± \frac{7}{6} = \frac{16}{6} or \frac{2}{6}\]

Answer 22

which simplifies to 8/3 and 1/3

Answer 23

x= 3^(8/3) or x= 3^(1/3)

Answer 24

why is t=1/2

Answer 25

I should have typed
\[ t= \frac{1}{2a}(-b ± \sqrt{b^2-4ac} ) \]
which is the quadratic formula

Answer 26

@phi why dont you directly factorise....
\[9t ^{2}-27t+8=0\]
\[9t ^{2}-24t-3t+8=0\]
\[3t(3t-8)-1(3t-8)=0\]
(3t-1)(3t-8)=0
t=1/3 and t=8/3

then...\[3^{x}=1/3 and 3^x=8/3

Answer 27

is not a 1
quadratic formula is
\[-b+-\sqrt{b2-4*a*c}/2*a\]

Answer 28

yes, but remember the -b is also divided by 2a

Answer 29

but t is not 1/2 . t is 1/3 or 8/3

as for how to solve this, use whatever method you are most comfortable with.
all variations: quadratic formula or factoring give the same answer.

Answer 30

\[9t ^{2}-27t+8=0\]

Use factorization:

\[9t^2 - 3t - 24t + 8 = 0\]

\[3t(3t-1) - 8(3t - 1) = 0 \implies (3t-1)(3t-8) = 0\]

\[t = \frac{1}{3} \qquad Or \qquad t = \frac{8}{3}\]

Answer 31

\[3^x = \frac{1}{3} \implies 3^x = 3^{-1} \implies x = -1\]

Answer 32

\[3^x = \frac{8}{3} \implies 3^{x+1} = 8\]

taking log(10):

\[\large (x+1) \cdot \log_{10}(3) = 3 \cdot \log_{10}(2)\]

\(log_{10} (3) = 0.4771 \) and \(log_{10}(2) = 0.3010\)

Put this values and solve for x now..

Answer 33

yupp..thanks

Answer 34

Welcome dear..

Answer 35

:)