Precalculus Examples

$\log (3) \cdot 5 + \log (3) \cdot 6$

Step 1

Simplify each term.

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Step 1.1

Multiply $\log (3) \cdot 5$ .

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Step 1.1.1

Reorder $\log (3)$ and $5$ .

$5 \cdot \log (3) + \log (3) \cdot 6$

Step 1.1.2

Simplify $5 \cdot \log (3)$ by moving $5$ inside the logarithm.

$\log (3^{5}) + \log (3) \cdot 6$

Step 1.2

Raise $3$ to the power of $5$ .

$\log (243) + \log (3) \cdot 6$

Step 1.3

Multiply $\log (3) \cdot 6$ .

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Step 1.3.1

Reorder $\log (3)$ and $6$ .

$\log (243) + 6 \cdot \log (3)$

Step 1.3.2

Simplify $6 \cdot \log (3)$ by moving $6$ inside the logarithm.

$\log (243) + \log (3^{6})$

Step 1.4

Raise $3$ to the power of $6$ .

$\log (243) + \log (729)$

Step 2

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

$\log (243 \cdot 729)$

Step 3

Multiply $243$ by $729$ .

$\log (177147)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (177147)$

Decimal Form:

$5.24833380 \dots$