A Tribute to Euler

Algebra Level 3

Find the number of real solutions of the equation e 3 x = 1 e^{3x}=-1 .

No solution 1 solution 2 solutions Infinitely many solutions

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2 solutions

Md Zuhair
Apr 24, 2017

Relevant wiki: Stretching Graphs

Its simply,

Here We can break it up into two parts,

y 1 = e 3 x y_1=e^{3x} and y 2 = 1 y_2=-1

For any x R x \in \mathbb{R} , we have y 1 y_1 to be positive, where as y_2 is always 1 -1 .So they will Never intersect. \boxed{\text{Never intersect.}}

Always in the habit of C \mathbb{C} , didn't even read that it was R \mathbb{R} . :P

Tapas Mazumdar - 4 years, 1 month ago
Mohan Nayak
Apr 24, 2017

to solve it graphically, the curve never touches the x-axis as it is asymptotic in nature. to solve it algebraically, ln on both sides, ln(e^3x)=ln(-1), 3x=ln(-1). ln of negative integers do not exist.Hence no solutions

good to see u on brilliant.

Ayush G Rai - 4 years, 1 month ago

same here.

mohan nayak - 4 years, 1 month ago

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