Precalculus Examples

$\frac{1}{3} \cdot \log_{2} (a) + \log_{2} (b + 1)$

Step 1

Simplify $\frac{1}{3} \log_{2} (a)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{2} (a^{\frac{1}{3}}) + \log_{2} (b + 1)$

Step 2

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

$\log_{2} (a^{\frac{1}{3}} (b + 1))$

Step 3

Apply the distributive property.

$\log_{2} (a^{\frac{1}{3}} b + a^{\frac{1}{3}} \cdot 1)$

Step 4

Simplify the expression.

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Step 4.1

Multiply $a^{\frac{1}{3}}$ by $1$ .

$\log_{2} (a^{\frac{1}{3}} b + a^{\frac{1}{3}})$

Step 4.2

Reorder factors in $\log_{2} (a^{\frac{1}{3}} b + a^{\frac{1}{3}})$ .

$\log_{2} (b a^{\frac{1}{3}} + a^{\frac{1}{3}})$