Express the quadratic equation $\displaystyle y = x^2 $as a linear equation using the substitution $\displaystyle s = ln y$, $\displaystyle t = ln x$. I have no idea how to start this. Any help is appreciated!
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Originally Posted by live_laugh_luv27 Express the quadratic equation $\displaystyle y = x^2 $as a linear equation using the substitution $\displaystyle s = ln y$, $\displaystyle t = ln x$. I have no idea how to start this. Any help is appreciated! Taking the natural log of both sides gives $\displaystyle \ln y = \ln x^2 = 2 \ln x$
Originally Posted by danny arrigo Taking the natural log of both sides gives $\displaystyle \ln y = \ln x^2 = 2 \ln x$ Ok...but where do the s and t come in??
Originally Posted by live_laugh_luv27 Ok...but where do the s and t come in?? If you let $\displaystyle s = \ln y\; \text{and}\; r = \ln x$ gives $\displaystyle s = 2r$, a linear equation.
Ok, thanks
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