Question 133321: Solve for x:2 to the power of x^2 -5x = 8
Please show steps
Thank you:)
Answer by nycsharkman(136)   (Show Source):
You can put this solution on YOUR website! What you have here is:
2^(x^2 -5x) = 8
After going back to the question, I realized that you are talking about an exponential equation.
This is totally different.
The first thing you want to do is create the same base on BOTH sides of the equation.
On the left side we have base 2.
How can we do that with 8?
What number multiplied by itself three times will produce 8?
How about 2? Yes, 2 to the third power = 8.
We now have this equation with the same base 2 on both sides:
2^(x^2 -5x) = 2^3
Since we now have the same base on both sides of the equation, simply EQUATE the exponents and solve for x.
x^2 - 5x = 3
x^2 - 5x - 3 = 0
This quadratic cannot be factored. In that case, you can complete the square or use the quadratic formula. The formula is easier to use.
x = -b + -sqr{b^2 - 4ac}/2a, where a = 1, b = -5 and c = -3
x = -(-5)+ - sqrt{(-5)^2 - 4(1)(-3)}/2(1)
x = 5 + - sqrt{25 + 12}/2
x = 5 + - sqrt{37}/2
We now separate x into a positive and negative answer.
x = 5 + sqrt{37}/2
OR
x = 5 - sqrt{37}/2
|
|
|
