Precalculus Examples

$\log_{2} (x - 2) (x - 9) = 3$

Step 1

Simplify $\log_{2} (x - 2) (x - 9)$ .

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Step 1.1

Apply the distributive property.

$\log_{2} (x - 2) x + \log_{2} (x - 2) \cdot - 9 = 3$

Step 1.2

Multiply $\log_{2} (x - 2) \cdot - 9$ .

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Step 1.2.1

Reorder $\log_{2} (x - 2)$ and $- 9$ .

$\log_{2} (x - 2) x - 9 \cdot \log_{2} (x - 2) = 3$

Step 1.2.2

Simplify $- 9 \cdot \log_{2} (x - 2)$ by moving $9$ inside the logarithm.

$\log_{2} (x - 2) x - \log_{2} ({(x - 2)}^{9}) = 3$

Step 1.3

Reorder factors in $\log_{2} (x - 2) x - \log_{2} ({(x - 2)}^{9})$ .

$x \log_{2} (x - 2) - \log_{2} ({(x - 2)}^{9}) = 3$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 2.71818672, 10$

Step 3