Precalculus Examples

$\log (\sqrt{5}) \cdot 25$

Step 1

Multiply $\log (\sqrt{5}) \cdot 25$ .

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Step 1.1

Reorder $\log (\sqrt{5})$ and $25$ .

$25 \cdot \log (\sqrt{5})$

Step 1.2

Simplify $25 \cdot \log (\sqrt{5})$ by moving $25$ inside the logarithm.

$\log ({\sqrt{5}}^{25})$

Step 2

Rewrite ${\sqrt{5}}^{25}$ as $\sqrt{5^{25}}$ .

$\log (\sqrt{5^{25}})$

Step 3

Raise $5$ to the power of $25$ .

$\log (\sqrt{298023223876953000})$

Step 4

Rewrite $298023223876953000$ as $10^{2} \cdot 2980232238769530$ .

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Step 4.1

Factor $100$ out of $298023223876953000$ .

$\log (\sqrt{100 (2980232238769530)})$

Step 4.2

Rewrite $100$ as $10^{2}$ .

$\log (\sqrt{10^{2} \cdot 2980232238769530})$

Step 5

Pull terms out from under the radical.

$\log (10 \sqrt{2980232238769530})$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\log (10 \sqrt{2980232238769530})$

Decimal Form:

$8.73712505 \dots$