Finite Math Examples

$\log (\sqrt{8}) N = 4$

Step 1

Divide each term in $\log (\sqrt{8}) N = 4$ by $\log (\sqrt{8})$ .

$\frac{\log (\sqrt{8}) N}{\log (\sqrt{8})} = \frac{4}{\log (\sqrt{8})}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $\log (\sqrt{8})$ .

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Step 2.1.1

Cancel the common factor.

$\frac{\log (\sqrt{8}) N}{\log (\sqrt{8})} = \frac{4}{\log (\sqrt{8})}$

Step 2.1.2

Divide $N$ by $1$ .

$N = \frac{4}{\log (\sqrt{8})}$

Step 3

Simplify the right side.

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Step 3.1

Simplify the denominator.

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Step 3.1.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 3.1.1.1

Factor $4$ out of $8$ .

$N = \frac{4}{\log (\sqrt{4 (2)})}$

Step 3.1.1.2

Rewrite $4$ as $2^{2}$ .

$N = \frac{4}{\log (\sqrt{2^{2} \cdot 2})}$

Step 3.1.2

Pull terms out from under the radical.

$N = \frac{4}{\log (2 \sqrt{2})}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$N = \frac{4}{\log (2 \sqrt{2})}$

Decimal Form:

$N = 8.85847491 \dots$