Algebra Examples

$2 \cdot \log_{4} (9) + 3 \cdot \log_{4} (2)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log_{4} (9)$ by moving $2$ inside the logarithm.

$\log_{4} (9^{2}) + 3 \cdot \log_{4} (2)$

Step 1.2

Raise $9$ to the power of $2$ .

$\log_{4} (81) + 3 \cdot \log_{4} (2)$

Step 1.3

Logarithm base $4$ of $2$ is $\frac{1}{2}$ .

$\log_{4} (81) + 3 \cdot \frac{1}{2}$

Step 1.4

Combine $3$ and $\frac{1}{2}$ .

$\log_{4} (81) + \frac{3}{2}$

Step 2

To write $\log_{4} (81)$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\log_{4} (81) \cdot \frac{2}{2} + \frac{3}{2}$

Step 3

Combine fractions.

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Step 3.1

Combine $\log_{4} (81)$ and $\frac{2}{2}$ .

$\frac{\log_{4} (81) \cdot 2}{2} + \frac{3}{2}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{\log_{4} (81) \cdot 2 + 3}{2}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $\log_{4} (81) \cdot 2$ .

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Step 4.1.1

Reorder $\log_{4} (81)$ and $2$ .

$\frac{2 \cdot \log_{4} (81) + 3}{2}$

Step 4.1.2

Simplify $2 \cdot \log_{4} (81)$ by moving $2$ inside the logarithm.

$\frac{\log_{4} (81^{2}) + 3}{2}$

Step 4.2

Raise $81$ to the power of $2$ .

$\frac{\log_{4} (6561) + 3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\log_{4} (6561) + 3}{2}$

Decimal Form:

$4.66992500 \dots$