Algebra Examples

$\log_{4} (3) + \frac{\log_{4} (5)}{3} + \frac{\log_{4} (7)}{3}$

Step 1

Combine the numerators over the common denominator.

$\log_{4} (3) + \frac{\log_{4} (5) + \log_{4} (7)}{3}$

Step 2

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

$\log_{4} (3) + \frac{\log_{4} (5 \cdot 7)}{3}$

Step 3

Multiply $5$ by $7$ .

$\log_{4} (3) + \frac{\log_{4} (35)}{3}$

Step 4

Simplify each term.

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Step 4.1

Rewrite $\frac{\log_{4} (35)}{3}$ as $\frac{1}{3} \log_{4} (35)$ .

$\log_{4} (3) + \frac{1}{3} \log_{4} (35)$

Step 4.2

Simplify $\frac{1}{3} \log_{4} (35)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{4} (3) + \log_{4} (35^{\frac{1}{3}})$

Step 5

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

$\log_{4} (3 \cdot 35^{\frac{1}{3}})$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\log_{4} (3 \cdot 35^{\frac{1}{3}})$

Decimal Form:

$1.64736175 \dots$