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If 4^x+y=1 and 4^x-y=4 , then the value of x and y will be respectively?
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If 4^x+y=1 and 4^x-y=4 , then the value of x and y will be respectivel...
Understanding the Equations
We have two equations to solve:
1. 4^x + y = 1
2. 4^x - y = 4
To find the values of x and y, let's analyze these equations step by step.
Step 1: Add the Equations
- When we add the two equations, we eliminate y:
(4^x + y) + (4^x - y) = 1 + 4
This simplifies to:
2 * 4^x = 5
Therefore:
4^x = 5/2
Step 2: Substitute Back to Find y
- Now, substitute 4^x into one of the original equations to find y. Using the first equation:
4^x + y = 1
(5/2) + y = 1
Thus:
y = 1 - 5/2
y = 1 - 2.5 = -1.5
Step 3: Find x
- We have already established that 4^x = 5/2. We can express x in terms of logarithm:
x = log4(5/2)
This can be calculated using the change of base formula if needed.
Final Values
- Therefore, the values of x and y are:
- x = log4(5/2)
- y = -1.5
These solutions satisfy both original equations, confirming their correctness.
We have two equations to solve:
1. 4^x + y = 1
2. 4^x - y = 4
To find the values of x and y, let's analyze these equations step by step.
Step 1: Add the Equations
- When we add the two equations, we eliminate y:
(4^x + y) + (4^x - y) = 1 + 4
This simplifies to:
2 * 4^x = 5
Therefore:
4^x = 5/2
Step 2: Substitute Back to Find y
- Now, substitute 4^x into one of the original equations to find y. Using the first equation:
4^x + y = 1
(5/2) + y = 1
Thus:
y = 1 - 5/2
y = 1 - 2.5 = -1.5
Step 3: Find x
- We have already established that 4^x = 5/2. We can express x in terms of logarithm:
x = log4(5/2)
This can be calculated using the change of base formula if needed.
Final Values
- Therefore, the values of x and y are:
- x = log4(5/2)
- y = -1.5
These solutions satisfy both original equations, confirming their correctness.
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If 4^x+y=1 and 4^x-y=4 , then the value of x and y will be respectively?
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If 4^x+y=1 and 4^x-y=4 , then the value of x and y will be respectively? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If 4^x+y=1 and 4^x-y=4 , then the value of x and y will be respectively? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 4^x+y=1 and 4^x-y=4 , then the value of x and y will be respectively?.
If 4^x+y=1 and 4^x-y=4 , then the value of x and y will be respectively? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If 4^x+y=1 and 4^x-y=4 , then the value of x and y will be respectively? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 4^x+y=1 and 4^x-y=4 , then the value of x and y will be respectively?.
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