Precalculus Examples

$\log_{7} (\frac{7 π}{4 k})$

Step 1

Rewrite $\log_{7} (\frac{7 π}{4 k})$ as $\log_{7} (7 π) - \log_{7} (4 k)$ .

$\log_{7} (7 π) - \log_{7} (4 k)$

Step 2

Rewrite $\log_{7} (7 π)$ as $\log_{7} (7) + \log_{7} (π)$ .

$\log_{7} (7) + \log_{7} (π) - \log_{7} (4 k)$

Step 3

Logarithm base $7$ of $7$ is $1$ .

$1 + \log_{7} (π) - \log_{7} (4 k)$

Step 4

Rewrite $\log_{7} (4 k)$ as $\log_{7} (4) + \log_{7} (k)$ .

$1 + \log_{7} (π) - (\log_{7} (4) + \log_{7} (k))$

Step 5

Simplify each term.

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Step 5.1

Simplify each term.

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Step 5.1.1

Rewrite $\log_{7} (4)$ as $\log_{7} (2^{2})$ .

$1 + \log_{7} (π) - (\log_{7} (2^{2}) + \log_{7} (k))$

Step 5.1.2

Expand $\log_{7} (2^{2})$ by moving $2$ outside the logarithm.

$1 + \log_{7} (π) - (2 \log_{7} (2) + \log_{7} (k))$

Step 5.2

Apply the distributive property.

$1 + \log_{7} (π) - (2 \log_{7} (2)) - \log_{7} (k)$

Step 5.3

Multiply $2$ by $- 1$ .

$1 + \log_{7} (π) - 2 \log_{7} (2) - \log_{7} (k)$