Solve for x 2^(x^2-3)=64

$2^{x^{2} - 3} = 64$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$2^{x^{2} - 3} = 2^{6}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x^{2} - 3 = 6$

Step 3

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Add $3$ to both sides of the equation.

$x^{2} = 6 + 3$

Add $6$ and $3$ .

$x^{2} = 9$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 3$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 3$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 3$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 3$