1. ## Given 2^x=8^(y+1)...

Given 2^x=8^(y+1) and 9^y=3^(x-9), find the value of x+7.

2. Originally Posted by ceasar_19134
Given 2^x=8^(y+1) and 9^y=3^(x-9), find the value of x+7.
2^x = 8^(y+1) is 2^x = 2^(3y+3) or x=3y+3.
9^y=3^(x-9) is 3^(2y) = 3^(x-9) or 2y=x-9.
Now solve that system.

3. 2^x = 8^(y+1) is 2^x = 2^(3y+3) ---> x=3y+3.....(1)
9^y=3^(x-9) is 3^(2y) = 3^(x-9) ---> 2y=x-9......(2)

(x-3)/3 = y

substitute this into (2)

(2x - 6)/3 = x - 9
2x - 6 = 3x - 27
x = 21 (and y = 6)
therefore
The text passage contains a mathematical problem involving solving a system of equations and finding the value of \( x + 7 \). The problem is presented in multiple parts, with the solution provided step-by-step.
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
1. ## Given 2^x=8^(y+1)...

Given 2^x=8^(y+1) and 9^y=3^(x-9), find the value of x+7.

2. Originally Posted by ceasar_19134
Given 2^x=8^(y+1) and 9^y=3^(x-9), find the value of x+7.
2^x = 8^(y+1) is 2^x = 2^(3y+3) or x=3y+3.
9^y=3^(x-9) is 3^(2y) = 3^(x-9) or 2y=x-9.
Now solve that system.

3. 2^x = 8^(y+1) is 2^x = 2^(3y+3) ---> x=3y+3.....(1)
9^y=3^(x-9) is 3^(2y) = 3^(x-9) ---> 2y=x-9......(2)

(x-3)/3 = y

substitute this into (2)

(2x - 6)/3 = x - 9
2x - 6 = 3x - 27
x = 21 (and y = 6)
therefore
user
The text passage contains a mathematical problem involving solving a system of equations and finding the value of \( x + 7 \). The problem is presented in multiple parts, with the solution provided step-by-step.

TYPE: SINGLE_QUESTION_WITH_ANSWER