Question

What are the solutions to the equation below: 4x^x+1 = 5^-x (100 points) THERE IS MORE THAN ONE ANSWER

Answer 1

$\\ \rm\rightarrowtail 4^{x+1}=5^{-x}$

$\\ \rm\rightarrowtail ln4^{x+1}=ln5^{-x}$

$\\ \rm\rightarrowtail (x+1)ln4=-xln5$

$\\ \rm\rightarrowtail xln4+ln4=-xln5$

$\\ \rm\rightarrowtail xln4+xln5=-ln4$

$\\ \rm\rightarrowtail x(ln4+ln5)=-ln4$

$\\ \rm\rightarrowtail x=\dfrac{-ln4}{ln4+ln5}$

$\\ \rm\rightarrowtail x=\dfrac{-ln4}{ln20}$

Option F is correct