Solving the Unknown for Indices

**Ogsta101** · January 27th 2008, 01:41 AM

Solve for 'x':

3^2x - 8.3^x - 9 = 0

**mr fantastic** · January 27th 2008, 01:53 AM

Originally Posted by Ogsta101

Solve for 'x':

3^2x - 8.3^x - 9 = 0

$3^{2x} - 8 \times 3^x - 9 = 0 \Rightarrow (3^x)^2 - 8 (3^x) - 9 = 0 \Rightarrow w^2 - 8w - 9 = 0$ where $w = 3^x$ .

After a bit more working:

Therefore $3^x = 9 = 3^2$ or $3^x = -1$ .

One of these has no real solutions. The other has one real solution.

Therefore x = ......

**Ogsta101** · January 27th 2008, 02:05 AM

Originally Posted by mr fantastic

$3^{2x} - 8 \times 3^x - 9 = 0 \Rightarrow (3^x)^2 - 8 (3^x) - 9 = 0 \Rightarrow w^2 - 8w - 9 = 0$ where $w = 3^x$ .

After a bit more working:

Therefore $3^x = 9 = 3^2$ or $3^x = -1$ .

One of these has no real solutions. The other has one real solution.

Therefore x = ......

Does x = 3???

I'm not completely sure because when I sub 3 back into the original question, it doesnt equal 0. So now I'm a little confused. But i do understand all the working...

**mr fantastic** · January 27th 2008, 03:08 AM

Originally Posted by Ogsta101

Does x = 3???

I'm not completely sure because when I sub 3 back into the original question, it doesnt equal 0. So now I'm a little confused. But i do understand all the working...

$3^x = 3^2$ . The bases are the same. What does x have to equal to make the indices the same?? Hint: NOT 3!!

**Ogsta101** · January 27th 2008, 03:15 AM

Originally Posted by mr fantastic

$3^x = 3^2$ . The bases are the same. What does x have to equal to make the indices the same?? Hint: NOT 3!!

Ugh - I did totally the wrong thing! Man I'm dumb. Ok I totally get it now!!!

Thanx sooooooooooo MUCH!!!

(x = 2 yeah?)

**mr fantastic** · January 27th 2008, 03:40 AM

Originally Posted by Ogsta101

Ugh - I did totally the wrong thing! Man I'm dumb. Ok I totally get it now!!!

Thanx sooooooooooo MUCH!!!

(x = 2 yeah?)

Yeah!

**Anita Wu** · May 1st 2009, 11:21 PM

how 2 solve: 4^x=32

**ADARSH** · May 2nd 2009, 02:03 AM

$4^x = (2^2)^x$

Knowing that
$32 = 2^5$
Thus

2^{2x} = 2^5

Hence

2x = 5

x = 5/2
_________
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