Finite Math Examples

$\log_{5} (x) = \log_{5} (9 + 2)$

Step 1

Subtract $\log_{5} (9 + 2)$ from both sides of the equation.

$\log_{5} (x) - \log_{5} (9 + 2) = 0$

Step 2

Simplify $\log_{5} (x) - \log_{5} (9 + 2)$ .

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Step 2.1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{5} (\frac{x}{9 + 2}) = 0$

Step 2.2

Add $9$ and $2$ .

$\log_{5} (\frac{x}{11}) = 0$

Step 3

Set the argument in $\log_{5} (\frac{x}{11})$ less than or equal to $0$ to find where the expression is undefined.

$\frac{x}{11} \leq 0$

Step 4

Solve for $x$ .

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Step 4.1

Multiply both sides by $11$ .

$\frac{x}{11} \cdot 11 \leq 0 \cdot 11$

Step 4.2

Simplify.

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Cancel the common factor of $11$ .

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Step 4.2.1.1.1

Cancel the common factor.

$\frac{x}{11} \cdot 11 \leq 0 \cdot 11$

Step 4.2.1.1.2

Rewrite the expression.

$x \leq 0 \cdot 11$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Multiply $0$ by $11$ .

$x \leq 0$

Step 5

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x \leq 0$

$(- \infty, 0]$

Step 6