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