Question

What is the solution of 2^x= -3x+ 5 ?Enter your answer.

Answer 1

x = 1

Explanation:

1. Graph each side of the equation. The solution is the x-value of the point of intersection.
2. Thus, x = 1

Answer 2

`2^x=-3x+5`

hence, we have

`1=((-3x+5))/(2^x)`

or equivalently

`\begin{gathered} 1=(-3x+5)e^(-x\ln 2)\ldots\ldots.(A) \\ \end{gathered}`

since

`\frac{1}{2^x^{}}=2^(-x)=e^(-x\ln 2)`

Now, from equation A, we can identify:

`\begin{gathered} u=(-x+(5)/(3))\ln (2) \\ \text{and} \\ x=-(3u-5\ln (2))/(3\ln (2)) \end{gathered}`

by substituying these equations into A, we have,

`1=(-3(-(3u-5\ln2)/(3\ln2))+5)e^{-\ln 2(-(3u-5\ln 2)/(3\ln 2))}`

by simplifying this equation, we have

`1=e^{(3u-5\ln2)/(3)}((3u-5\ln 2)/(\ln 2)+5)`

The final solution is

`x=-(3W((e^(5\ln2/3)\ln2)/(3))-5\ln 2)/(3\ln 2)`

where W is given by

`W=\frac{e^(-5\ln 2/3+2)}{e^{(3u-5\ln 2+6)/(5)}}`