Precalculus Examples

$\log_{2} (3 z) + \log_{2} (y) + 3 \log_{2} (z)$

Step 1

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

$\log_{2} (3 z y) + 3 \log_{2} (z)$

Step 2

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

$\log_{2} (3 z y) + \log_{2} (z^{3})$

Step 3

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

$\log_{2} (3 z y z^{3})$

Step 4

Multiply $z$ by $z^{3}$ by adding the exponents.

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Step 4.1

Move $z^{3}$ .

$\log_{2} (3 (z^{3} z) y)$

Step 4.2

Multiply $z^{3}$ by $z$ .

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Step 4.2.1

Raise $z$ to the power of $1$ .

$\log_{2} (3 (z^{3} z^{1}) y)$

Step 4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\log_{2} (3 z^{3 + 1} y)$

Step 4.3

Add $3$ and $1$ .

$\log_{2} (3 z^{4} y)$