Algebra Examples

$\log_{11} (x) + \log_{11} (10 x - 1) = 1$

Step 1

Subtract $1$ from both sides of the equation.

$\log_{11} (x) + \log_{11} (10 x - 1) - 1 = 0$

Step 2

Simplify $\log_{11} (x) + \log_{11} (10 x - 1) - 1$ .

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Step 2.1

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

$\log_{11} (x (10 x - 1)) - 1 = 0$

Step 2.2

Simplify each term.

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Step 2.2.1

Apply the distributive property.

$\log_{11} (x (10 x) + x \cdot - 1) - 1 = 0$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$\log_{11} (10 x \cdot x + x \cdot - 1) - 1 = 0$

Step 2.2.3

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

$\log_{11} (10 x \cdot x - 1 \cdot x) - 1 = 0$

Step 2.2.4

Simplify each term.

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Step 2.2.4.1

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

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Step 2.2.4.1.1

Move $x$ .

$\log_{11} (10 (x \cdot x) - 1 \cdot x) - 1 = 0$

Step 2.2.4.1.2

Multiply $x$ by $x$ .

$\log_{11} (10 x^{2} - 1 \cdot x) - 1 = 0$

Step 2.2.4.2

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

$\log_{11} (10 x^{2} - x) - 1 = 0$

Step 3

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 4

The standard form is $\log_{11} (10 x^{2} - x) - 1$ .

$\log_{11} (10 x^{2} - x) - 1 = 0$

Step 5