Basic Math Examples

$9^{2 y} = 27$

Step 1

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

$3^{2 (2 y)} = 3^{3}$

Step 2

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

$2 (2 y) = 3$

Step 3

Solve for $y$ .

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Step 3.1

Multiply $2$ by $2$ .

$4 \cdot y = 3$

Step 3.2

Divide each term in $4 \cdot y = 3$ by $4$ and simplify.

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Step 3.2.1

Divide each term in $4 \cdot y = 3$ by $4$ .

$\frac{4 \cdot y}{4} = \frac{3}{4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{4 \cdot y}{4} = \frac{3}{4}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{3}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{3}{4}$

Decimal Form:

$y = 0.75$