Precalculus Examples

$6 \log_{6} (2) - \log_{6} (x) - \log_{6} (23)$

Step 1

Simplify each term.

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Step 1.1

Simplify $6 \log_{6} (2)$ by moving $6$ inside the logarithm.

$\log_{6} (2^{6}) - \log_{6} (x) - \log_{6} (23)$

Step 1.2

Raise $2$ to the power of $6$ .

$\log_{6} (64) - \log_{6} (x) - \log_{6} (23)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{6} (\frac{64}{x}) - \log_{6} (23)$

Step 3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{6} (\frac{\frac{64}{x}}{23})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\log_{6} (\frac{64}{x} \cdot \frac{1}{23})$

Step 5

Multiply $\frac{64}{x}$ by $\frac{1}{23}$ .

$\log_{6} (\frac{64}{x \cdot 23})$

Step 6

Move $23$ to the left of $x$ .

$\log_{6} (\frac{64}{23 x})$