I cannot figure this out for the life of me!!! HELP!?

Question

Can you help me with this? We're supposed to show all our work, but I cannot figure this out!

Solve for x:
(e^4)^x * e^x2 = 12

Note: The asterisk mark (*) is supposed to be a multiplication sign... I just couldn't find a better way to show that.

Answer 1

Use properties of exponents to simplify

(e^4)^x * e^x2 = 12

e^4x (e^(x^2) = 12

e^(4x + x^2) = 12

Take the natural log of both sides

ln e^(4x + x^2) = ln 12

4x + x^2 = ln 12

x^2 + 4x - ln 12 = 0

Either graph and find the zeros of the graph or solve using the quadratic formula.

x is approximately -4.547 or .547

Answer 2

That is just the same as: e^4x × e^2x = 12

Remember the exponents of identical bases can be combined…so it would then reduce to:

e^6x = 12 (the reason I added the exponents was because the “e’s” were being multiplied…if the “e’s” were being divided, i would have 2 subtract the exponents…I’m sure u’ve learned these rules in ur algebra textbook, anyway…

then take the log(to base e) of both sides and then u get an equation that looks like this (log to base e is known as the natural log which is specified as “ln” on ur graphics calculator:

6x log(base e) e = log(base e) 12

log(base e) e = 1
log(base e) 12 = 2.48490665 (u can work this out on ur graphics calculator)

6x = 2.48490665 (now divide both sides by 6 and ur answer will be…)
X = 0.4142 (rounded to four decimal places)

Hope this helps =D

Answer 3

(e^4)^x * e^x2 = 12
I am assuming that e^x2 means e^(x^2). Hopefully that's a right assumption or you can ignore everything else!

First, multiply the powers on the far left term:

e^(4x)*e(x^2) = 12

Then combine the two terms on the left:

e^(x^2 + 4x) = 12

Now take the natural log of both sides:

x^2 + 4x = ln12
x^2 + 4x - ln12 = 0

Now just use the quadratic formula with a=1, b=4, c= -ln12.

Answer 4

(e^4)^x e^x² = 12

Simplifying:

e^(4x) e^x² = 12
e^(4x+x²) = 12

Taking natural log of both sides:

x²+4x=ln 12

Complete the square:

x²+4x+4 = 4+ln 12

Factor:

(x+2)² = 4+ln 12

Take the square roots:

x+2 = ±√(4+ln 12)

Subtract 2 from both sides:

x = -2±√(4+ln 12)

And we are done.

Answer 5

Take the natural log of both sides of the equation.

Answer 6

(e^4)^x=e^4x
e^4x*e^(x^2) = e^(4x+x^2) =12

takin ln
x^2+4x-ln12 = 0
x=((-4+-sqrt(16+4ln12)/2 =-2+-sqrt(4+ln12)
x=-2+sqrt(4+ln12)= 05465 x=-2-sqrt(4+ln12) =-4,5465

Answer 7

ummm what is ^?? division?? i got 2e^x*=24??? probably not right, but it is pretty hard! good luck