Consider the following non linear equation where x is the independent variable, y is the dependent variabie, and A and e are constants. y=-Ax^B Which of the following is the resulting gradient variable in linearised form? Select one: a)log 10(B) b)A c)exp(B) d)B e)log(-A)

link223mh

link223mh

Answered question

2022-10-29

Consider the following non linear equation where x is the independent variable, y is the dependent variabie, and A and e are constants.
y = A x B
Which of the following is the resulting gradient variable in linearised form?
Select one:
a ) l o g   10 ( B ) b ) A c ) e x p ( B ) d ) B e ) l o g ( A )

Answer & Explanation

Theresa Wade

Theresa Wade

Beginner2022-10-30Added 9 answers

For a linear equation of the form: y=mx+b, the slope or the gradient is m and the y-intercept is b.
Using the properties of the logarithmic functions, it can be written that:
log ( a b ) = log a + log b log a b = b ( log a )
Take logarithm on both sides of the equation: y = A x B and simplify to obtain the linear form of this equation. Use the properties of the logarithmic functions for simplification.
y = A x B log y = log ( A x B ) = log ( A ) + log ( x B ) = log ( A ) + B ( log x ) = B ( log x ) + log ( A )
The linearised form is log y = B ( log x ) + log ( A ). This equation is similar to the linear equation: y=mx+b. Hence, it can be concluded that the gradient variable is B.
Hence, the correct option is d. Since c is correct, other options are incorrect.

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