Basic Math Examples

$3^{5 q} = 9^{3 q + 1}$

Step 1

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

$3^{5 q} = 3^{2 (3 q + 1)}$

Step 2

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

$5 q = 2 (3 q + 1)$

Step 3

Solve for $q$ .

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Step 3.1

Simplify $2 (3 q + 1)$ .

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Step 3.1.1

Apply the distributive property.

$5 q = 2 (3 q) + 2 \cdot 1$

Step 3.1.2

Multiply.

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Step 3.1.2.1

Multiply $3$ by $2$ .

$5 q = 6 q + 2 \cdot 1$

Step 3.1.2.2

Multiply $2$ by $1$ .

$5 q = 6 q + 2$

Step 3.2

Move all terms containing $q$ to the left side of the equation.

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Step 3.2.1

Subtract $6 q$ from both sides of the equation.

$5 q - 6 q = 2$

Step 3.2.2

Subtract $6 q$ from $5 q$ .

$- q = 2$

Step 3.3

Divide each term in $- q = 2$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- q = 2$ by $- 1$ .

$\frac{- q}{- 1} = \frac{2}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{q}{1} = \frac{2}{- 1}$

Step 3.3.2.2

Divide $q$ by $1$ .

$q = \frac{2}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $2$ by $- 1$ .

$q = - 2$