# Indices (simple but i am have problems)

Printable View

• Jan 8th 2012, 09:14 AM
kingmaths
Indices (simple but i am getting problems)
9^x+1 - 13(3^x) + 4 =0

Use y = 3^x

OK so i start and reached to this point
3^2(x+1) - 13(3^x) + 4 = 0

3^2x+2 - 13(3^x) + 4 = 0

I need some help to proceed, thanks in advance
• Jan 8th 2012, 09:34 AM
Bacterius
Re: Indices (simple but i am have problems)
$3^{2x + 2} - 13 \times 3^x + 4 = 0$

Expand:

$3^{2x} \times 3^2 - 13 \times 3^x + 4 = 0$

Which becomes (from the rules of indices - look at the first term):

$\left (3^{x} \right )^2 \times 3^2 - 13 \times 3^x + 4 = 0$

Now use the hint and substitute $y= 3^x$

$y^2 \times 3^2 - 13y + 4 = 0$

So:

$9 y^2 - 13y + 4 = 0$

Can you solve for $y$ and put the solution back in terms of $x$ now?
The text contains a mathematical problem involving indices and a request for help to proceed with the solution. An answer or further steps to solve the problem are provided in the response.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Indices (simple but i am have problems)

Printable View

• Jan 8th 2012, 09:14 AM
kingmaths
Indices (simple but i am getting problems)
9^x+1 - 13(3^x) + 4 =0

Use y = 3^x

OK so i start and reached to this point
3^2(x+1) - 13(3^x) + 4 = 0

3^2x+2 - 13(3^x) + 4 = 0

I need some help to proceed, thanks in advance
• Jan 8th 2012, 09:34 AM
Bacterius
Re: Indices (simple but i am have problems)
$3^{2x + 2} - 13 \times 3^x + 4 = 0$

Expand:

$3^{2x} \times 3^2 - 13 \times 3^x + 4 = 0$

Which becomes (from the rules of indices - look at the first term):

$\left (3^{x} \right )^2 \times 3^2 - 13 \times 3^x + 4 = 0$

Now use the hint and substitute $y= 3^x$

$y^2 \times 3^2 - 13y + 4 = 0$

So:

$9 y^2 - 13y + 4 = 0$

Can you solve for $y$ and put the solution back in terms of $x$ now?
user
The text contains a mathematical problem involving indices and a request for help to proceed with the solution. An answer or further steps to solve the problem are provided in the response.

TYPE: SINGLE_QUESTION_WITH_ANSWER