SOLUTION: Please solve the following equation: {{{(sqrt(3))^(x+2)/27^x=3^(-x^2) }}} I am stumped as to how this can be solved. First, I did this: {{{(sqrt(3))^(x+2)/3^(3)^(x)=3^(-x^2) }

Question 853665: Please solve the following equation:

I am stumped as to how this can be solved.
First, I did this:

Then:

Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!

=
=
=

(2x - 1)*(x - 2) = 0
x = 1/2
x = 2
You can check both answers.
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Those two steps are good. Now the right member becomes .

Revising the equation then you have:

You can make the left member be the base of 3, raised to a power:

----rendering cuts off the top; 3^((x+2)/2)=3^(3^x-x^2)

The left member is 3 raised to a power; the right member is 3 also raised to a power. Those powers, exponents, are equal.

Still not easy to solve.

-----No ordinary algebra steps for this. Left and right members are separate functions which have one or more points (maybe) of intersection.
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