Finite Math Examples

$\log_{2} (x) + \log_{2} (10 x - 1) = 1$

Step 1

Simplify $\log_{2} (x) + \log_{2} (10 x - 1)$ .

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Step 1.1

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

$\log_{2} (x (10 x - 1)) = 1$

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

$\log_{2} (x (10 x) + x \cdot - 1) = 1$

Step 1.2.2

Reorder.

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Step 1.2.2.1

Rewrite using the commutative property of multiplication.

$\log_{2} (10 x \cdot x + x \cdot - 1) = 1$

Step 1.2.2.2

Move $- 1$ to the left of $x$ .

$\log_{2} (10 x \cdot x - 1 \cdot x) = 1$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $x$ by $x$ by adding the exponents.

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Step 1.3.1.1

Move $x$ .

$\log_{2} (10 (x \cdot x) - 1 \cdot x) = 1$

Step 1.3.1.2

Multiply $x$ by $x$ .

$\log_{2} (10 x^{2} - 1 \cdot x) = 1$

Step 1.3.2

Rewrite $- 1 x$ as $- x$ .

$\log_{2} (10 x^{2} - x) = 1$

Step 2

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

$x = \frac{1}{2}$

Step 3