Solve the exponential equation, and express in exact form only.

e^(4x^2 - 11) = 8

Question

Solve the exponential equation, and express in exact form only.

e^(4x^2 - 11) = 8

amistre64 · Answer

how do we undo that "e" to get to the "x" ?

ahh ... thats better :)

anonymous · Answer

take the ln of both sides

anonymous · Answer

I've been trying to figure that out? I know that if they have the same base I would be able to solve it, but I'm quite confused.

amistre64 · Answer

dapauls right, we can take the natural log of both sides.  the ln function undoes the "e" function

anonymous · Answer

In(e^4x^2-11)/In8

amistre64 · Answer

$$exp(4x^2 - 11) = 8$$
$$ln(exp(4x^2 - 11)) = ln(8)$$
$$4x^2 - 11 = ln(8)$$

and the rest is what it is

anonymous · Answer

exactly amistre64

anonymous · Answer

$$4x^2 - 11= 2.7094 $$

I would add 11 and divide by 4, then take the square.

amistre64 · Answer

yep, and depending on how exacting your text requires; it might want a plus/minus applied to the sqrt

amistre64 · Answer

x^2 = 7

x = sqrt(7) is called the ... principal root i think, but:

x = +- sqrt(7)  gives all the results

anonymous · Answer

ok. Thanks!