Exponential Equations

[greatwhiteshark]

Exponential Equations

8^xsquared - 2x = 1/2

My Work:

I converted the above this way:

8^xsquared/8^-2x = 1/2

I then cross-multiplied:

8^xsquared (2) = 8^-2x (1)

16^xsquared = 8^-2x

I converted 16 and 8 into equal bases.

2^4^(xsquared) = 2^3(-2x)

I then equated exponents.

4x^2 = -6x

I moved -6x to the left side of the equation.

4x^2 + 6x = 0

I factored.

2x (2x + 3) = 0

I set each to equal zero.

2x = 0 and 2x + 3 = 0

x = 0 = one solution

However, I found that x = -3/2 for equation 2x + 3 = 0 is NOT the correct solution. What am I doing wrong?

 

[tkhunny]

Exponential Equations
8^xsquared - 2x = 1/2

Pretty tough to read. Do you mean:

8^{x^2 - 2x} = 1/2?
Adding parentheses would have helped.
8^(xsquared - 2x) = 1/2

8^xsquared/8^-2x = 1/2

Whoops. You wandered off already. You can have either of these:
(8^(xsquared))*8^(-2x) = 1/2 or
(8^(xsquared))/8^(2x) = 1/2

I then cross-multiplied:

Never say that. I causes me pain. There are many operations with which one can "do the same thing to both sides." "Cross multiply" is NOT one of them.

Anyway, this isn't getting anywhere, since it already strayed.

8^{x^2 - 2x} = 1/2

Why not convert to Equal Bases right up front?

(2³)^{x^2 - 2x} = 2^-1

So, if the expressions are equal and the bases are equal, the exponents must be equal, too.

3*(8x^2 - 2x) = -1

You can hande the rest.

 

[greatwhiteshark]

yes

Yes, I can handle the rest.
I forgot that 1/2 is also written 2^-1

 

[Guest]

can someone help me with this problem y-2=1-y
- - -
5 5 3

 

[Guest]

can somebody help me y/5-2/5=1/3-y

 

[tkhunny]

can somebody help me y/5-2/5=1/3-y

Don't hijack threads. Very irritating.

Please supply more parentheses for clarity. For example, is the Right-Hand-Side one of these?

(1/3) - y ??

1/(3-y) ??

It makes a BIG difference.

 

[Denis]

On Janet's 8^(x^2 - 2x) = 1/2

Another way:
x^2 - 2x = log(1/2) / log(8)
x^2 - 2x = -1/3
x^2 - 2x + 1/3 = 0
3x^2 - 6x + 1 = 0 ; finish off using quadratic...