Precalculus Examples

$9^{t} = 27$

Step 1

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

$3^{2 t} = 3^{3}$

Step 2

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

$2 t = 3$

Step 3

Divide each term in $2 t = 3$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 t = 3$ by $2$ .

$\frac{2 t}{2} = \frac{3}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 t}{2} = \frac{3}{2}$

Step 3.2.1.2

Divide $t$ by $1$ .

$t = \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = \frac{3}{2}$

Decimal Form:

$t = 1.5$

Mixed Number Form:

$t = 1 \frac{1}{2}$