Basic Math Examples

$40 = 5 \cdot 2^{n}$

Step 1

Rewrite the equation as $5 \cdot 2^{n} = 40$ .

$5 \cdot 2^{n} = 40$

Step 2

Divide each term in $5 \cdot 2^{n} = 40$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 \cdot 2^{n} = 40$ by $5$ .

$\frac{5 \cdot 2^{n}}{5} = \frac{40}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 \cdot 2^{n}}{5} = \frac{40}{5}$

Step 2.2.1.2

Divide $2^{n}$ by $1$ .

$2^{n} = \frac{40}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $40$ by $5$ .

$2^{n} = 8$

Step 3

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

$2^{n} = 2^{3}$

Step 4

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

$n = 3$