Convert this non-linear equation into a linear equation

Linear, quadratic, module, parametric equations

Convert this non-linear equation into a linear equation

Postby Guest » Thu Feb 18, 2021 9:04 pm

Non-linear equation: y=bx^n
Reduce this non-linear equation to the linear form Y=mX+c, where X and Y represent the functions of x or y or both and m and c as constants.

If you know how to solve this, please help! Thank you very much.
Guest
 

Re: Convert this non-linear equation into a linear equation

Postby Baltuilhe » Fri Feb 19, 2021 2:29 pm

Good afternoon!!

[tex]y=bx^n[/tex]

Apply log in both sides:
[tex]\log(y)=\log\left(bx^n\right)\\
\log(y)=\log(b)+\log\left(x^n\right)\\
\log(y)=\log(b)+n\log(x)\\
\begin{cases}Y=\log(y)\\m=n\\X=\log(x)\\c=\log(b)\end{cases}\\
\boxed{Y=c+mX}[/tex]

Hope to Have Helped! (3H)

Baltuilhe
 
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