Question

Solve the exponential equation. Express your solutions in exact form only. Please show all of your work.

2e^x=(√10) e^x +3 Solve the exponential equation. Express your solutions in exact form only. Please show all of your work.

2e^x=(√10) e^x +3 @Mathematics

Answer 1

like solving
\[2z=\sqrt{10}z+3\] then replace z by
\[e^x\] and solve for x using logs

Answer 2

2e^x=(√10) e^x +3
2e^x-(√10) e^x =3
e^x[2-(√10) ] =3
e^x=3/[2-(√10) ] taking ln on both sides
x=ln{3/[2-(√10) ]}

Answer 3

wait a second

Answer 4

there is no solution to this because you have
\[e^x=\frac{3}{2-\sqrt{10}}\] which is a negative number and
\[e^x>0\] for all x