Precalculus Examples

$\log_{4} (10) + 3 \log_{4} (11) + 6 \log_{4} (3)$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \log_{4} (11)$ by moving $3$ inside the logarithm.

$\log_{4} (10) + \log_{4} (11^{3}) + 6 \log_{4} (3)$

Step 1.2

Raise $11$ to the power of $3$ .

$\log_{4} (10) + \log_{4} (1331) + 6 \log_{4} (3)$

Step 1.3

Simplify $6 \log_{4} (3)$ by moving $6$ inside the logarithm.

$\log_{4} (10) + \log_{4} (1331) + \log_{4} (3^{6})$

Step 1.4

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

$\log_{4} (10) + \log_{4} (1331) + \log_{4} (729)$

Step 2

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

$\log_{4} (10 \cdot 1331) + \log_{4} (729)$

Step 3

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

$\log_{4} (10 \cdot 1331 \cdot 729)$

Step 4

Multiply $10 \cdot 1331 \cdot 729$ .

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Step 4.1

Multiply $10$ by $1331$ .

$\log_{4} (13310 \cdot 729)$

Step 4.2

Multiply $13310$ by $729$ .

$\log_{4} (9702990)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log_{4} (9702990)$

Decimal Form:

$11.60499897 \dots$