Simplifying and Solving Exponential Expressions: Tips and Tricks

[amd123]

1. (3*square root of 2)^square root of 2 How do I simplify this and other exponential expressions?
2. 3^(power of 2*x)-1=3^(power of x) + 2 How do i solve this?

I don't know how to attempt it...Help please

 

[Manchot]

Regarding your first question: you can't, really. Subjectively, there's no "simpler" form than what you already have.

Regarding your second question: define y=3^x, and recast your equation in terms of y. Can you solve this?

 

[amd123]

according to glencoe algebra 2 number 1 can be simplified even more but they don't tell HOW?

no https://www.physicsforums.com/latex_images/16/1681321-1.png that's what its supposed to look like, i have to find x

 

[symbolipoint]

Try this: instead of 2^(1/2), use some variable, r, for the (1/2). Now you have
something like (3*2^r)^(2^r), convert this into ordinary algebraic notation so it is easier to understand; and then use your laws of exponents.

 

[symbolipoint]

Actually what I obtain is not much clearer. Example seems like a calculator exercise.

 

[symbolipoint]

Now, I find this:

(3^(1/2))*2^((2^(1/2))/2 )

It would look better if I had access to TEX right now.
Three to the square root of two power, multiplied by two to the [square root of two] over two power. It may read complicated, but it looks neat on my paper.

 

[Pere Callahan]

Now, I find this:

(3^(1/2))*2^((2^(1/2))/2 )

It would look better if I had access to TEX right now.

You can always use latex in your posts by typing your latex code [ /tex]. (without the space in front of the /)