Question

Use your calculator to solve -5e^(-4x+2)+3= 1/2log( (x^2) +1) and describe the steps you used. Round your answer to three decimals

Answer 1

Newton's approximation?

Answer 2

\[-5e^{-4x+2}+3= \frac{1}{2}\log( (x^2) +1 \\ \\ -5(e^{-4x} ~\times e^2)+3=\frac{1}{2} \log_{10}(x^2)+1 \\ \\ -10e^2e^{-4x}+4=\log_{10}(x^2) \\ \\ Using~\log~rule~a^b=c~ \implies \log_a(c)=b, \\ \\ 10^{-10e^2e^{-4x}+4}=x^2 \\ \\ x=\sqrt{10^{-10e^2e^{-4x}+4}}\]

Answer 3

Now, what you have to do is find the values of x, when x is 1,2,3,4,5...