Precalculus Examples

$\log_{2} ({(x)}^{2}) + \log_{2} (x - 6) = 0$

Step 1

Simplify $\log_{2} ({(x)}^{2}) + \log_{2} (x - 6)$ .

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Step 1.1

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

$\log_{2} ({(x)}^{2} (x - 6)) = 0$

Step 1.2

Apply the distributive property.

$\log_{2} (x^{2} x + x^{2} \cdot - 6) = 0$

Step 1.3

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.3.1

Multiply $x^{2}$ by $x$ .

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Step 1.3.1.1

Raise $x$ to the power of $1$ .

$\log_{2} (x^{2} x^{1} + x^{2} \cdot - 6) = 0$

Step 1.3.1.2

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

$\log_{2} (x^{2 + 1} + x^{2} \cdot - 6) = 0$

Step 1.3.2

Add $2$ and $1$ .

$\log_{2} (x^{3} + x^{2} \cdot - 6) = 0$

Step 1.4

Move $- 6$ to the left of $x^{2}$ .

$\log_{2} (x^{3} - 6 x^{2}) = 0$

Step 2

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

$x \approx 6.02752466$

Step 3