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If the equation y = abx can be written in linear form Y = A+BX, what are Y, X, A, B?
- a)Y = logy, X=x, A=loga and B=logb
- b)Y=y, A=a, B=b and X=x
- c)Y = y, A=a, B=logb and X=logx
- d)Y = logy, A=a, B=logb and X=x
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the equation y = abx can be written in linear form Y = A+BX, what a...
The given curve is y = abx.
Taking log on bothe the sides, we get,
logy = loga + x logb.
This can be written in the format of Y=A+BX
where
Y = logy, X = x, A = loga and B = logb.
Taking log on bothe the sides, we get,
logy = loga + x logb.
This can be written in the format of Y=A+BX
where
Y = logy, X = x, A = loga and B = logb.
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Community Answer
If the equation y = abx can be written in linear form Y = A+BX, what a...
To understand why the correct answer is option 'A', let's break down the equation y = abx and its linear form Y = ABX.
Given equation: y = abx
Linear form: Y = ABX
Identifying the variables:
- In the given equation, y is the dependent variable.
- In the linear form, Y is the dependent variable.
- In both equations, x is the independent variable.
- In the given equation, a and b are constants.
- In the linear form, A and B are constants.
Now let's analyze each option to see which one correctly represents the variables:
Option 'A':
- Y = logy: This represents the dependent variable in the linear form, which is correct.
- X = x: This represents the independent variable in both the given equation and the linear form, which is correct.
- A = loga: This represents one of the constants in the given equation, which is correct.
- B = logb: This represents the other constant in the given equation, which is correct.
Option 'B':
- Y = y: This represents the dependent variable in the linear form, which is correct.
- A = a: This represents one of the constants in the given equation, which is correct.
- B = b: This represents the other constant in the given equation, which is correct.
- X = x: This represents the independent variable in both the given equation and the linear form, which is correct.
Option 'C':
- Y = y: This represents the dependent variable in the linear form, which is correct.
- A = a: This represents one of the constants in the given equation, which is correct.
- B = logb: This represents the other constant in the given equation, which is incorrect. The correct representation would be B = b.
Option 'D':
- Y = logy: This represents the dependent variable in the linear form, which is correct.
- A = a: This represents one of the constants in the given equation, which is correct.
- B = logb: This represents the other constant in the given equation, which is correct.
- X = x: This represents the independent variable in both the given equation and the linear form, which is correct.
From the analysis above, we can conclude that the correct answer is option 'A' because it correctly represents all the variables in the given equation and its linear form.
Given equation: y = abx
Linear form: Y = ABX
Identifying the variables:
- In the given equation, y is the dependent variable.
- In the linear form, Y is the dependent variable.
- In both equations, x is the independent variable.
- In the given equation, a and b are constants.
- In the linear form, A and B are constants.
Now let's analyze each option to see which one correctly represents the variables:
Option 'A':
- Y = logy: This represents the dependent variable in the linear form, which is correct.
- X = x: This represents the independent variable in both the given equation and the linear form, which is correct.
- A = loga: This represents one of the constants in the given equation, which is correct.
- B = logb: This represents the other constant in the given equation, which is correct.
Option 'B':
- Y = y: This represents the dependent variable in the linear form, which is correct.
- A = a: This represents one of the constants in the given equation, which is correct.
- B = b: This represents the other constant in the given equation, which is correct.
- X = x: This represents the independent variable in both the given equation and the linear form, which is correct.
Option 'C':
- Y = y: This represents the dependent variable in the linear form, which is correct.
- A = a: This represents one of the constants in the given equation, which is correct.
- B = logb: This represents the other constant in the given equation, which is incorrect. The correct representation would be B = b.
Option 'D':
- Y = logy: This represents the dependent variable in the linear form, which is correct.
- A = a: This represents one of the constants in the given equation, which is correct.
- B = logb: This represents the other constant in the given equation, which is correct.
- X = x: This represents the independent variable in both the given equation and the linear form, which is correct.
From the analysis above, we can conclude that the correct answer is option 'A' because it correctly represents all the variables in the given equation and its linear form.
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