Algebra Examples

(2, 25)

$(2, 25)$

Step 1

To find an exponential function,

f (x) = a^{x}

$f (x) = a^{x}$ , containing the point, set

f (x)

$f (x)$ in the function to the

y

$y$ value

25

$25$ of the point, and set

x

$x$ to the

x

$x$ value

2

$2$ of the point.

25 = a^{2}

$25 = a^{2}$

Step 2

Solve the equation for

a

$a$ .

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Step 2.1

Rewrite the equation as

a^{2} = 25

$a^{2} = 25$ .

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}

$a = \pm \sqrt{25}$

Step 2.3

Simplify

\pm \sqrt{25}

$\pm \sqrt{25}$ .

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Step 2.3.1

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

a = \pm \sqrt{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

$a = \pm 5$

a = \pm 5

$a = \pm 5$

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

$\pm$ to find the first solution.

a = 5

$a = 5$

Step 2.4.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

a = - 5

$a = - 5$

Step 2.4.3

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

a = 5, - 5

$a = 5, - 5$

a = 5, - 5

$a = 5, - 5$

a = 5, - 5

$a = 5, - 5$

Step 3

Substitute each value for

a

$a$ back into the function

f (x) = a^{x}

$f (x) = a^{x}$ to find each possible exponential function.

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

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

(2, 25)

$(2, 25)$

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