Precalculus Examples

$\log (2) \cdot 4 + \log (5) \cdot 4$

Step 1

Simplify each term.

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Step 1.1

Multiply $\log (2) \cdot 4$ .

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Step 1.1.1

Reorder $\log (2)$ and $4$ .

$4 \cdot \log (2) + \log (5) \cdot 4$

Step 1.1.2

Simplify $4 \cdot \log (2)$ by moving $4$ inside the logarithm.

$\log (2^{4}) + \log (5) \cdot 4$

Step 1.2

Raise $2$ to the power of $4$ .

$\log (16) + \log (5) \cdot 4$

Step 1.3

Multiply $\log (5) \cdot 4$ .

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Step 1.3.1

Reorder $\log (5)$ and $4$ .

$\log (16) + 4 \cdot \log (5)$

Step 1.3.2

Simplify $4 \cdot \log (5)$ by moving $4$ inside the logarithm.

$\log (16) + \log (5^{4})$

Step 1.4

Raise $5$ to the power of $4$ .

$\log (16) + \log (625)$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (16 \cdot 625)$

Step 3

Multiply $16$ by $625$ .

$\log (10000)$

Step 4

Logarithm base $10$ of $10000$ is $4$ .

$4$