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If the equation y=axb can be written in the linear form Y=A+BX, what are Y, X, A, B?
- a)Y=logy, A=loga, B=b and X=logx
- 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=axb can be written in the linear form Y=A+BX, what a...
Explanation:
To understand the given equation and its linear form, let's break down the components:
Given equation: y = ax^b
Linear form: Y = A BX
Components of the linear form:
- Y: Dependent variable (output variable)
- X: Independent variable (input variable)
- A: Intercept (constant)
- B: Slope (coefficient)
Now, let's compare the given equation with the linear form:
Comparison:
- y = ax^b (given equation)
- Y = A BX (linear form)
Dependent Variable:
In the given equation, the dependent variable is "y". Similarly, in the linear form, the dependent variable is "Y".
Independent Variable:
In the given equation, the independent variable is "x". Similarly, in the linear form, the independent variable is "X".
Intercept:
In the given equation, there is no intercept term explicitly mentioned. However, in the linear form, the intercept term is denoted by "A".
Slope:
In the given equation, the coefficient of "x" is denoted as "a". Similarly, in the linear form, the coefficient of "X" is denoted as "B".
Transformation:
To transform the given equation into the linear form, we need to take logarithms of both sides:
log(y) = log(ax^b)
Resultant equation:
By applying the logarithmic transformation, the equation becomes:
Y = log(y)
X = log(x)
A = log(a)
B = b
Therefore, the correct answer is option 'A':
Y = log(y)
X = log(x)
A = log(a)
B = b
To understand the given equation and its linear form, let's break down the components:
Given equation: y = ax^b
Linear form: Y = A BX
Components of the linear form:
- Y: Dependent variable (output variable)
- X: Independent variable (input variable)
- A: Intercept (constant)
- B: Slope (coefficient)
Now, let's compare the given equation with the linear form:
Comparison:
- y = ax^b (given equation)
- Y = A BX (linear form)
Dependent Variable:
In the given equation, the dependent variable is "y". Similarly, in the linear form, the dependent variable is "Y".
Independent Variable:
In the given equation, the independent variable is "x". Similarly, in the linear form, the independent variable is "X".
Intercept:
In the given equation, there is no intercept term explicitly mentioned. However, in the linear form, the intercept term is denoted by "A".
Slope:
In the given equation, the coefficient of "x" is denoted as "a". Similarly, in the linear form, the coefficient of "X" is denoted as "B".
Transformation:
To transform the given equation into the linear form, we need to take logarithms of both sides:
log(y) = log(ax^b)
Resultant equation:
By applying the logarithmic transformation, the equation becomes:
Y = log(y)
X = log(x)
A = log(a)
B = b
Therefore, the correct answer is option 'A':
Y = log(y)
X = log(x)
A = log(a)
B = b
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Community Answer
If the equation y=axb can be written in the linear form Y=A+BX, what a...
The given curve is y=axb.
Taking log on bothe the sides, we get,
logy = loga + blogx.
This can be written as Y=A+BX,
where
Y=logy, A=loga, B=b and X=logx.
Taking log on bothe the sides, we get,
logy = loga + blogx.
This can be written as Y=A+BX,
where
Y=logy, A=loga, B=b and X=logx.
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If the equation y=axb can be written in the linear form Y=A+BX, what are Y, X, A, B?a)Y=logy, A=loga, B=b and X=logxb)Y=y, A=a, B=b and X=xc)Y=y, A=a, B=logb and X=logxd)Y=logy, A=a, B=logb and X=xCorrect answer is option 'A'. Can you explain this answer?
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