Precalculus Examples

$2 \log_{4} (7) + \frac{\log_{4} (8)}{2}$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log_{4} (7)$ by moving $2$ inside the logarithm.

$\log_{4} (7^{2}) + \frac{\log_{4} (8)}{2}$

Step 1.2

Raise $7$ to the power of $2$ .

$\log_{4} (49) + \frac{\log_{4} (8)}{2}$

Step 1.3

Rewrite $\frac{\log_{4} (8)}{2}$ as $\frac{1}{2} \log_{4} (8)$ .

$\log_{4} (49) + \frac{1}{2} \log_{4} (8)$

Step 1.4

Simplify $\frac{1}{2} \log_{4} (8)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{4} (49) + \log_{4} (8^{\frac{1}{2}})$

Step 2

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

$\log_{4} (49 \cdot 8^{\frac{1}{2}})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\log_{4} (49 \cdot 8^{\frac{1}{2}})$

Decimal Form:

$3.55735492 \dots$