Algebra Examples

$(2, 25)$

Step 1

To find an exponential function, $f (x) = a^{x}$ , containing the point, set $f (x)$ in the function to the $y$ value $25$ of the point, and set $x$ to the $x$ value $2$ of the point.

$25 = a^{2}$

Step 2

Solve the equation for $a$ .

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Step 2.1

Rewrite the equation as $a^{2} = 25$ .

$a^{2} = 25$

Step 2.2

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

$a = \pm \sqrt{25}$

Step 2.3

Simplify $\pm \sqrt{25}$ .

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Step 2.3.1

Rewrite $25$ as $5^{2}$ .

$a = \pm \sqrt{5^{2}}$

Step 2.3.2

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

$a = \pm 5$

Step 2.4

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

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Step 2.4.1

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

$a = 5$

Step 2.4.2

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

$a = - 5$

Step 2.4.3

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

$a = 5, - 5$

Step 3

Substitute each value for $a$ back into the function $f (x) = a^{x}$ to find each possible exponential function.

$f (x) = {(5)}^{x}, f (x) = {(- 5)}^{x}$