Finite Math Examples

$9^{\frac{x - 5}{4}} = 9^{\frac{1}{2}}$

Step 1

Simplify $9^{\frac{1}{2}}$ .

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Step 1.1

Simplify the expression.

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Step 1.1.1

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

$9^{\frac{x - 5}{4}} = {(3^{2})}^{\frac{1}{2}}$

Step 1.1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$9^{\frac{x - 5}{4}} = 3^{2 (\frac{1}{2})}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Cancel the common factor.

$9^{\frac{x - 5}{4}} = 3^{2 (\frac{1}{2})}$

Step 1.2.2

Rewrite the expression.

$9^{\frac{x - 5}{4}} = 3^{1}$

Step 1.3

Evaluate the exponent.

$9^{\frac{x - 5}{4}} = 3$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 7$

Step 3