Precalculus Examples

$9 \log (b y) + 8 \log (b Z)$

Step 1

Simplify each term.

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Step 1.1

Simplify $9 \log (b y)$ by moving $9$ inside the logarithm.

$\log ({(b y)}^{9}) + 8 \log (b Z)$

Step 1.2

Apply the product rule to $b y$ .

$\log (b^{9} y^{9}) + 8 \log (b Z)$

Step 1.3

Simplify $8 \log (b Z)$ by moving $8$ inside the logarithm.

$\log (b^{9} y^{9}) + \log ({(b Z)}^{8})$

Step 1.4

Apply the product rule to $b Z$ .

$\log (b^{9} y^{9}) + \log (b^{8} Z^{8})$

Step 2

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

$\log (b^{9} y^{9} (b^{8} Z^{8}))$

Step 3

Multiply $b^{9}$ by $b^{8}$ by adding the exponents.

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Step 3.1

Move $b^{8}$ .

$\log (b^{8} b^{9} y^{9} Z^{8})$

Step 3.2

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

$\log (b^{8 + 9} y^{9} Z^{8})$

Step 3.3

Add $8$ and $9$ .

$\log (b^{17} y^{9} Z^{8})$