Precalculus Examples

$5 \log_{a} (z + 7) + \log_{a} (2 z + 9)$

Step 1

Simplify $5 \log_{a} (z + 7)$ by moving $5$ inside the logarithm.

$\log_{a} ({(z + 7)}^{5}) + \log_{a} (2 z + 9)$

Step 2

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

$\log_{a} ({(z + 7)}^{5} (2 z + 9))$

Step 3

Apply the distributive property.

$\log_{a} ({(z + 7)}^{5} (2 z) + {(z + 7)}^{5} \cdot 9)$

Step 4

Reorder.

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Step 4.1

Rewrite using the commutative property of multiplication.

$\log_{a} (2 {(z + 7)}^{5} z + {(z + 7)}^{5} \cdot 9)$

Step 4.2

Move $9$ to the left of ${(z + 7)}^{5}$ .

$\log_{a} (2 {(z + 7)}^{5} z + 9 \cdot {(z + 7)}^{5})$

Step 4.3

Reorder factors in $\log_{a} (2 {(z + 7)}^{5} z + 9 {(z + 7)}^{5})$ .

$\log_{a} (2 z {(z + 7)}^{5} + 9 {(z + 7)}^{5})$