Basic Math Examples

$6^{5 n + 6} = 1296$

Step 1

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

$6^{5 n + 6} = 6^{4}$

Step 2

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

$5 n + 6 = 4$

Step 3

Solve for $n$ .

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Step 3.1

Move all terms not containing $n$ to the right side of the equation.

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Step 3.1.1

Subtract $6$ from both sides of the equation.

$5 n = 4 - 6$

Step 3.1.2

Subtract $6$ from $4$ .

$5 n = - 2$

Step 3.2

Divide each term in $5 n = - 2$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 n = - 2$ by $5$ .

$\frac{5 n}{5} = \frac{- 2}{5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 n}{5} = \frac{- 2}{5}$

Step 3.2.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 2}{5}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$n = - \frac{2}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{2}{5}$

Decimal Form:

$n = - 0.4$