Algebra Examples

$2 \log (4) + 3 \log (2)$

Step 1

Simplify each term.

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Step 1.1

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

$\log (4^{2}) + 3 \log (2)$

Step 1.2

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

$\log (16) + 3 \log (2)$

Step 1.3

Simplify $3 \log (2)$ by moving $3$ inside the logarithm.

$\log (16) + \log (2^{3})$

Step 1.4

Raise $2$ to the power of $3$ .

$\log (16) + \log (8)$

Step 2

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

$\log (16 \cdot 8)$

Step 3

Multiply $16$ by $8$ .

$\log (128)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (128)$

Decimal Form:

$2.10720996 \dots$